All Markets
Gyanesh Jain
2024-09-01
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final_function <- function(file_path){
df=read.csv(file_path) %>% as_tibble()
df <- df %>% mutate(quantity = as.numeric(quantity))
df <- df %>% mutate(price = as.numeric(price))
market = df$Market[1]
df = df %>% group_by(Date) %>% summarise(quantity = sum(quantity), price = max(price))
df1=zoo(df$price,order.by=as.Date(df$Date,format="%d-%b-%y"))
df2=zoo(df$quantity,order.by=as.Date(df$Date,format="%d-%b-%y"))
df1=na.omit(df1)
df2=na.omit(df2)
x=dsa(df1)
pre_quantity=dsa(df2)
quantity_pre1=pre_quantity$sa_result$seas_adj
x6=x$sa_result$seas_adj
data=na.omit(abs(diff(x6,1)))
print(adf.test(data$seas_adj))
print(pp.test(data$seas_adj))
quantity=na.omit(abs(diff(quantity_pre1,1)))
print(adf.test(quantity$seas_adj))
print(pp.test(quantity$seas_adj))
p=ggplot(data,aes(x=seas_adj))+geom_density(n=131072)
v=ggplot_build(p)
final_data=cbind.data.frame(v$data[[1]]$x,v$data[[1]]$y,v$data[[1]]$density)
colnames(final_data)=c("X","Y","Density")
x_dif=diff(final_data$X,1)
y_dif=diff(final_data$Y,1)
if(round(max(final_data$Y),1)==0){
round2=3
}else{round2=2}
maxy=which.max(final_data$Y)
miny=which(final_data$Y<1e-03)
miny=min(miny)
a1<-which.min(final_data$X[c(maxy:miny)])
a2<-which.max(final_data$X[c(maxy:miny)])
a1<-c(final_data$X[a1],final_data$Y[a1])
a2<-c(final_data$X[a2],final_data$Y[a2])
a0<-rbind(a1,a2)
a3<-lm(a0[,2]~a0[,1])$coef
a4<-c(-a3[2],1)
a4<-a4/sqrt(sum(a4**2))
a5<-which.min(cbind(final_data$X,final_data$Y)%*%a4)
final_data=final_data %>% mutate (sno=row_number())
slope=round(y_dif/x_dif,3)
final_data1=cbind.data.frame(x_dif,y_dif,slope)
final_data=final_data[-1,]
data_analysis=cbind.data.frame(final_data,final_data1)
round1=7
data_analysis=data_analysis %>% mutate(diffrentiator=case_when(slope>0~"NA",(slope==0 & Y<0.8*max(data_analysis$Y))~"B",TRUE~"A"))
data_analysis=data_analysis %>% mutate(area=Y*x_dif)
sumAB=(data_analysis %>% filter(diffrentiator!="NA")%>% summarise(sumAB=sum(area)))$sumAB
sumA=(data_analysis %>% filter(diffrentiator=="A") %>% summarise(sumAB=sum(area)))$sumAB
ratio1=sumA/sumAB
sumAx=(data_analysis %>% filter(diffrentiator=="A") %>% summarise(sumAB=sum(X)))$sumAB
sumABx=(data_analysis %>% filter(diffrentiator!="NA") %>% summarise(sumAB=sum(X)))$sumAB
# meanA=sumA/count(data_analysis %>% filter(diffrentiator=="A") %>% select(Y))$n
# meanAB=sumAB/count(data_analysis %>% filter(diffrentiator!="NA") %>% select(Y))$n
# arrA=sum(((data_analysis %>% filter(diffrentiator=="A") %>% select(Y))-meanA)^2)
# arrAB=sum(((data_analysis %>% filter(diffrentiator!="NA") %>% select(Y))-meanAB)^2)
varA=(data_analysis %>% filter(diffrentiator=="A") %>% summarise(sumAB=var(area)))$sumAB
varB=(data_analysis %>% filter(diffrentiator!="B") %>% summarise(sumAB=var(area)))$sumAB
varAplusB=varA + varB
varAB=(data_analysis %>% filter(diffrentiator!="NA") %>% summarise(sumAB=var(area)))$sumAB
collusion=(sumA/sumAB)*(varA/varAplusB)
A_df=data_analysis %>% filter(diffrentiator=="A") %>% filter(area>10^-round1)
AB_df=data_analysis %>% filter(diffrentiator!="NA") %>% filter(area>10^-round1)
A_df=A_df %>% mutate(xy=X*Y)
AB_df=AB_df %>% mutate(xy=X*Y)
meanA1=sum(A_df$xy)/sum(A_df$Y)
meanAB1=sum(AB_df$xy)/sum(AB_df$Y)
A_df=A_df %>% mutate(varn=Y*(X-meanA1)^2)
AB_df=AB_df %>% mutate(varn=Y*(X-meanA1)^2)
varA1=sum(A_df$varn)/sum(A_df$Y)
varAB1=sum(AB_df$varn)/sum(AB_df$Y)
ratio=sum(A_df$xy)/sum(AB_df$xy)
collusion1=ratio*min(varA1/varAB1,1)
fin_graph = ggplot(data_analysis,aes(x=X,y=Y,fill=diffrentiator))+geom_area(col="black")+scale_fill_manual(values=c("red", "yellow", "azure2"))+theme_classic(base_size=10)+
ggtitle(paste0(market))
print(fin_graph)
ggplotly(fin_graph)
ratio3=varA/varAplusB
output_df=tibble(sumA,sumAB,collusionmeasure1=ratio1,varA=format(varA,format="e",digits=2),varB=format(varB,format="e",digits=2),varAplusB=format(varAplusB,format="e",digits=2),varratio=format(ratio3,format="e",digits=2),varAB=format(varAB,format="e",digits=2),collusionmeasure2=collusion)
print(output_df)
(datatable(output_df))
print(summary(lm(quantity$seas_adj~data$seas_adj)))
print(summary(lm(log(quantity$seas_adj)~data$seas_adj)))
quantity_diff=diff(log(quantity$seas_adj))
price_diff=diff(log(x6))
new_df=cbind.data.frame(price_diff[1:length(quantity_diff)],quantity_diff)
colnames(new_df)=c("price","quantity")
models <- auto_ardl(quantity~price, data = new_df, max_order = 10)
print(models)
ardl=models$best_model
print(summary(ardl))
print(pacf(na.omit(new_df$quantity),title="Quantity"))
print(acf(na.omit(new_df$quantity),title="Quantity"))
ar=arima(na.omit(new_df$quantity),order=c(5,0,0))
print(summary(ar))
print(ArchTest(quantity_diff,lags=5,demean=T))
ehatsq=ar$residuals^2
arch1=dynlm(ehatsq~L(ehatsq)+L(ehatsq,k=-2)+L(ehatsq,k=-3)+L(ehatsq,k=-4)+L(ehatsq,k=-5),data=ehatsq)
print(summary(arch1))
colnames(new_df)=c("log(diff(price))","log(diff(quantity))")
plot.ts(new_df)}final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market1.csv")## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `quantity = as.numeric(quantity)`.
## Caused by warning:
## ! NAs introduced by coercion## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -9.8967, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -4281.8, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -8.4166, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -3807.6, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary
## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.587 0.667 0.879 3.4e-08 3.6e-08 7e-08 0.49 2.6e-09
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.059 -1.118 -0.983 -0.575 85.592
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.131310 0.062911 17.98 <2e-16 ***
## data$seas_adj 0.041640 0.002571 16.20 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.761 on 3946 degrees of freedom
## Multiple R-squared: 0.06234, Adjusted R-squared: 0.06211
## F-statistic: 262.4 on 1 and 3946 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.9862 -1.0153 -0.0476 0.9090 5.4931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.420589 0.029037 -48.92 <2e-16 ***
## data$seas_adj 0.022771 0.001187 19.19 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.736 on 3946 degrees of freedom
## Multiple R-squared: 0.08536, Adjusted R-squared: 0.08513
## F-statistic: 368.3 on 1 and 3946 DF, p-value: < 2.2e-16
##
## $best_model
##
## Time series regression with "ts" data:
## Start = 12, End = 3948
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## -0.002425 -0.836548 -0.698725 -0.577070
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.515711 -0.470522 -0.318283 -0.114941
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.105644 -0.112337 -0.058034 0.644118
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.055423 2.290050 -0.823813 0.548551
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## -0.589573 1.817967 -0.732613 0.229483
## L(price, 9) L(price, 10)
## -0.179546 -0.751213
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 14109.36
## 2 9 6 14117.12
## 3 9 7 14118.37
## 4 9 8 14120.34
## 5 9 9 14122.34
## 6 7 10 14133.37
## 7 6 10 14134.30
## 8 8 6 14134.38
## 9 7 9 14135.10
## 10 8 7 14135.25
## 11 7 8 14135.79
## 12 6 9 14135.82
## 13 6 8 14136.50
## 14 7 7 14137.19
## 15 8 8 14137.21
## 16 6 7 14137.93
## 17 6 6 14140.03
## 18 5 10 14332.20
## 19 5 9 14334.50
## 20 5 8 14336.60
##
##
## Time series regression with "ts" data:
## Start = 12, End = 3948
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.4785 -0.7665 0.1517 0.9302 5.7290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.002425 0.023075 -0.105 0.916300
## L(quantity, 1) -0.836548 0.015960 -52.416 < 2e-16 ***
## L(quantity, 2) -0.698725 0.020766 -33.648 < 2e-16 ***
## L(quantity, 3) -0.577070 0.023528 -24.527 < 2e-16 ***
## L(quantity, 4) -0.515711 0.025215 -20.453 < 2e-16 ***
## L(quantity, 5) -0.470522 0.026036 -18.072 < 2e-16 ***
## L(quantity, 6) -0.318283 0.026035 -12.225 < 2e-16 ***
## L(quantity, 7) -0.114941 0.025201 -4.561 5.25e-06 ***
## L(quantity, 8) -0.105644 0.023497 -4.496 7.12e-06 ***
## L(quantity, 9) -0.112337 0.020736 -5.418 6.41e-08 ***
## L(quantity, 10) -0.058034 0.015937 -3.641 0.000275 ***
## price 0.644118 0.878007 0.734 0.463228
## L(price, 1) -0.055423 0.893259 -0.062 0.950530
## L(price, 2) 2.290050 0.892328 2.566 0.010314 *
## L(price, 3) -0.823813 0.894470 -0.921 0.357104
## L(price, 4) 0.548551 0.895751 0.612 0.540313
## L(price, 5) -0.589573 0.892382 -0.661 0.508861
## L(price, 6) 1.817967 0.894382 2.033 0.042155 *
## L(price, 7) -0.732613 0.893287 -0.820 0.412191
## L(price, 8) 0.229483 0.892066 0.257 0.797000
## L(price, 9) -0.179546 0.888047 -0.202 0.839786
## L(price, 10) -0.751213 0.873004 -0.860 0.389571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.448 on 3915 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.4309, Adjusted R-squared: 0.4279
## F-statistic: 141.2 on 21 and 3915 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.484 -0.328 -0.216 -0.154 -0.217 -0.223 -0.028 -0.010 -0.066 -0.057 -0.020
## 12 13 14 15 16 17 18 19 20 21 22
## -0.071 -0.088 0.017 -0.017 -0.023 0.007 -0.060 -0.012 -0.075 -0.009 0.030
## 23 24 25 26 27 28 29 30 31 32 33
## 0.029 -0.001 -0.011 -0.023 -0.078 -0.026 0.043 0.017 -0.054 0.034 -0.004
## 34 35
## -0.033 0.000## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.484 -0.017 0.022 -0.004 -0.067 0.020 0.119 -0.071 -0.039 0.033
## 11 12 13 14 15 16 17 18 19 20 21
## 0.007 -0.056 0.027 0.080 -0.081 0.005 0.034 -0.058 0.038 -0.034 0.074
## 22 23 24 25 26 27 28 29 30 31 32
## -0.028 -0.012 -0.008 -0.005 -0.007 -0.016 0.067 0.004 -0.044 -0.029 0.074
## 33 34 35
## -0.062 0.000 0.062
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7797 -0.6087 -0.4422 -0.3156 -0.2166 -0.0003
## s.e. 0.0155 0.0192 0.0204 0.0193 0.0156 0.0071
##
## sigma^2 estimated as 2.223: log likelihood = -7177.88, aic = 14369.76
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 503.17, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3942
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.553 -1.840 -1.265 0.257 60.330
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.70339 0.09443 18.039 < 2e-16 ***
## L(ehatsq) 0.05316 0.01589 3.346 0.000828 ***
## L(ehatsq, k = -2) 0.07848 0.01593 4.928 8.66e-07 ***
## L(ehatsq, k = -3) 0.01692 0.01597 1.059 0.289508
## L(ehatsq, k = -4) 0.06461 0.01594 4.052 5.17e-05 ***
## L(ehatsq, k = -5) 0.02144 0.01594 1.345 0.178704
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.922 on 3935 degrees of freedom
## Multiple R-squared: 0.01614, Adjusted R-squared: 0.01489
## F-statistic: 12.91 on 5 and 3935 DF, p-value: 1.77e-12
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market2.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -7.3639, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -4721.8, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -4.7663, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -4014.5, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.492 0.758 0.649 1.3e-06 1.5e-06 2.8e-06 0.45 9.6e-09
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -286.7 -285.7 -282.1 -245.4 21429.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 286.72823 22.04269 13.008 <2e-16 ***
## data$seas_adj -0.04797 0.02778 -1.727 0.0843 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1339 on 3799 degrees of freedom
## Multiple R-squared: 0.0007843, Adjusted R-squared: 0.0005213
## F-statistic: 2.982 on 1 and 3799 DF, p-value: 0.08429
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6312 -2.1167 -0.7795 1.9444 8.6990
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.287e+00 4.973e-02 25.876 < 2e-16 ***
## data$seas_adj -2.573e-04 6.267e-05 -4.106 4.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.021 on 3799 degrees of freedom
## Multiple R-squared: 0.004418, Adjusted R-squared: 0.004155
## F-statistic: 16.86 on 1 and 3799 DF, p-value: 4.116e-05## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3801
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## 0.003893 -0.679812 -0.616234 -0.528485
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.441802 -0.417166 -0.351064 -0.126048
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.062333 -0.031608 -0.043994 0.052330
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.046963 0.115404 0.064758 0.030704
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## 0.088509 0.418879 0.167692 -0.044838
## L(price, 9) L(price, 10)
## -0.292452 -0.267082
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 13432.49
## 2 8 10 13435.21
## 3 9 10 13437.21
## 4 7 10 13437.22
## 5 6 10 13456.64
## 6 8 9 13467.66
## 7 9 9 13469.65
## 8 7 9 13469.75
## 9 8 8 13487.63
## 10 7 8 13490.02
## 11 6 9 13490.85
## 12 7 7 13509.11
## 13 6 8 13511.31
## 14 6 7 13530.27
## 15 6 6 13553.41
## 16 5 10 13693.83
## 17 5 9 13726.43
## 18 5 8 13745.60
## 19 5 7 13766.24
## 20 5 6 13787.93
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3801
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.7608 -0.9402 0.1198 1.0010 9.1573
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.003893 0.029246 0.133 0.89410
## L(quantity, 1) -0.679812 0.017084 -39.792 < 2e-16 ***
## L(quantity, 2) -0.616234 0.020655 -29.835 < 2e-16 ***
## L(quantity, 3) -0.528485 0.023169 -22.810 < 2e-16 ***
## L(quantity, 4) -0.441802 0.024766 -17.839 < 2e-16 ***
## L(quantity, 5) -0.417166 0.025188 -16.562 < 2e-16 ***
## L(quantity, 6) -0.351064 0.025197 -13.933 < 2e-16 ***
## L(quantity, 7) -0.126048 0.024799 -5.083 3.92e-07 ***
## L(quantity, 8) -0.062333 0.023155 -2.692 0.00714 **
## L(quantity, 9) -0.031608 0.020629 -1.532 0.12556
## L(quantity, 10) -0.043994 0.017029 -2.584 0.00982 **
## price 0.052330 0.154699 0.338 0.73518
## L(price, 1) -0.046963 0.179759 -0.261 0.79391
## L(price, 2) 0.115404 0.182958 0.631 0.52823
## L(price, 3) 0.064758 0.182900 0.354 0.72331
## L(price, 4) 0.030704 0.172737 0.178 0.85893
## L(price, 5) 0.088509 0.166072 0.533 0.59410
## L(price, 6) 0.418879 0.167478 2.501 0.01243 *
## L(price, 7) 0.167692 0.173518 0.966 0.33390
## L(price, 8) -0.044838 0.174825 -0.256 0.79760
## L(price, 9) -0.292452 0.173191 -1.689 0.09139 .
## L(price, 10) -0.267082 0.165853 -1.610 0.10741
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.71 on 3407 degrees of freedom
## (362 observations deleted due to missingness)
## Multiple R-squared: 0.35, Adjusted R-squared: 0.346
## F-statistic: 87.37 on 21 and 3407 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.377 -0.290 -0.223 -0.134 -0.165 -0.274 -0.063 -0.038 0.002 -0.051 -0.035
## 12 13 14 15 16 17 18 19 20 21 22
## -0.078 -0.123 0.001 -0.005 0.007 -0.031 -0.054 -0.078 -0.068 -0.009 -0.006
## 23 24 25 26 27 28 29 30 31 32 33
## -0.004 -0.026 -0.052 -0.061 -0.037 0.000 0.010 0.012 -0.045 -0.026 -0.017
## 34 35
## -0.071 0.054## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.377 -0.107 -0.014 0.035 -0.053 -0.089 0.173 -0.013 -0.011 -0.058
## 11 12 13 14 15 16 17 18 19 20 21
## 0.029 -0.038 -0.044 0.121 -0.016 -0.005 -0.047 0.004 -0.022 -0.002 0.070
## 22 23 24 25 26 27 28 29 30 31 32
## -0.004 -0.004 -0.037 -0.010 -0.014 0.018 0.048 0.002 -0.005 -0.057 0.018
## 33 34 35
## -0.006 -0.031 0.114
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.6044 -0.5025 -0.3728 -0.2306 -0.1656 0.0011
## s.e. 0.0160 0.0184 0.0192 0.0184 0.0160 0.0101
##
## sigma^2 estimated as 3.21: log likelihood = -7608.12, aic = 15230.25
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 179.68, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3795
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.860 -2.430 -1.645 0.252 78.786
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.88784 0.13945 13.538 < 2e-16 ***
## L(ehatsq) 0.21674 0.01583 13.695 < 2e-16 ***
## L(ehatsq, k = -2) 0.10286 0.01619 6.355 2.33e-10 ***
## L(ehatsq, k = -3) 0.02278 0.01653 1.378 0.1682
## L(ehatsq, k = -4) 0.03370 0.01653 2.039 0.0415 *
## L(ehatsq, k = -5) 0.03587 0.01623 2.210 0.0272 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.529 on 3788 degrees of freedom
## Multiple R-squared: 0.07135, Adjusted R-squared: 0.07012
## F-statistic: 58.21 on 5 and 3788 DF, p-value: < 2.2e-16
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market3.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -6.4331, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -5110.6, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -5.9874, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -2972.2, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.250 0.752 0.333 0.00015 0.00015 3e-04 0.5 3.3e-07
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4034.6 -118.2 -118.0 -116.6 19764.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.182e+02 1.528e+01 7.737 1.28e-14 ***
## data$seas_adj 3.333e-03 3.293e-04 10.121 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 961.5 on 3997 degrees of freedom
## Multiple R-squared: 0.02499, Adjusted R-squared: 0.02474
## F-statistic: 102.4 on 1 and 3997 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.7650 -1.9035 -0.7541 1.8221 10.3044
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.238e-01 4.755e-02 -8.913 <2e-16 ***
## data$seas_adj 1.382e-05 1.025e-06 13.482 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.992 on 3997 degrees of freedom
## Multiple R-squared: 0.04349, Adjusted R-squared: 0.04326
## F-statistic: 181.8 on 1 and 3997 DF, p-value: < 2.2e-16## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3999
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3) L(quantity, 4)
## 0.005564 -0.848167 -0.756864 -0.703124 -0.619933
## L(quantity, 5) L(quantity, 6) L(quantity, 7) L(quantity, 8) price
## -0.532733 -0.459135 -0.109162 -0.050878 0.115676
## L(price, 1) L(price, 2) L(price, 3) L(price, 4) L(price, 5)
## -0.051263 0.069627 -0.019978 0.067260 0.109446
## L(price, 6) L(price, 7) L(price, 8) L(price, 9) L(price, 10)
## 0.042168 -0.053180 -0.081089 0.081367 0.082238
##
##
## $best_order
## quantity price
## 8 10
##
## $top_orders
## quantity price AIC
## 1 8 10 12983.62
## 2 9 10 12984.17
## 3 10 10 12984.72
## 4 7 10 12990.95
## 5 8 9 13001.46
## 6 9 9 13001.89
## 7 6 10 13004.76
## 8 7 9 13008.86
## 9 8 8 13020.63
## 10 6 9 13022.62
## 11 7 8 13028.03
## 12 6 8 13041.59
## 13 7 7 13049.08
## 14 6 7 13062.69
## 15 6 6 13084.33
## 16 5 10 13526.08
## 17 5 9 13545.47
## 18 5 8 13565.72
## 19 5 7 13588.53
## 20 5 6 13610.64
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3999
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.2619 -0.7338 0.1274 0.8898 5.6217
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.005564 0.024382 0.228 0.81951
## L(quantity, 1) -0.848167 0.016681 -50.846 < 2e-16 ***
## L(quantity, 2) -0.756864 0.021807 -34.707 < 2e-16 ***
## L(quantity, 3) -0.703124 0.024010 -29.285 < 2e-16 ***
## L(quantity, 4) -0.619933 0.025198 -24.602 < 2e-16 ***
## L(quantity, 5) -0.532733 0.025191 -21.147 < 2e-16 ***
## L(quantity, 6) -0.459135 0.024009 -19.124 < 2e-16 ***
## L(quantity, 7) -0.109162 0.021820 -5.003 5.92e-07 ***
## L(quantity, 8) -0.050878 0.016688 -3.049 0.00231 **
## price 0.115676 0.132677 0.872 0.38334
## L(price, 1) -0.051263 0.137861 -0.372 0.71003
## L(price, 2) 0.069627 0.138441 0.503 0.61504
## L(price, 3) -0.019978 0.138103 -0.145 0.88499
## L(price, 4) 0.067260 0.147637 0.456 0.64872
## L(price, 5) 0.109446 0.150270 0.728 0.46646
## L(price, 6) 0.042168 0.152643 0.276 0.78237
## L(price, 7) -0.053180 0.159776 -0.333 0.73928
## L(price, 8) -0.081089 0.160879 -0.504 0.61427
## L(price, 9) 0.081367 0.161863 0.503 0.61521
## L(price, 10) 0.082238 0.153037 0.537 0.59104
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.462 on 3583 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.4621, Adjusted R-squared: 0.4593
## F-statistic: 162 on 19 and 3583 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.463 -0.300 -0.243 -0.190 -0.174 -0.407 -0.047 -0.038 -0.025 -0.014 -0.020
## 12 13 14 15 16 17 18 19 20 21 22
## -0.045 -0.184 0.004 -0.024 0.004 0.040 -0.032 0.005 -0.132 0.041 -0.009
## 23 24 25 26 27 28 29 30 31 32 33
## 0.012 -0.010 -0.040 0.016 -0.087 0.024 -0.016 -0.006 0.015 0.012 -0.025
## 34 35 36
## -0.047 0.025 0.001## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.463 -0.021 -0.023 0.010 -0.012 -0.154 0.316 -0.126 -0.008 -0.016
## 11 12 13 14 15 16 17 18 19 20 21
## 0.000 -0.017 -0.114 0.250 -0.111 0.017 -0.006 -0.046 0.032 -0.136 0.255
## 22 23 24 25 26 27 28 29 30 31 32
## -0.130 0.033 -0.026 -0.026 0.047 -0.142 0.226 -0.119 0.037 -0.012 -0.024
## 33 34 35 36
## 0.004 -0.084 0.186 -0.104
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7538 -0.5958 -0.4643 -0.3159 -0.1746 -0.0005
## s.e. 0.0156 0.0190 0.0199 0.0190 0.0156 0.0075
##
## sigma^2 estimated as 2.447: log likelihood = -7462.15, aic = 14938.3
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 483.69, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3993
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.710 -1.991 -1.428 0.165 96.918
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.86022 0.10925 17.027 < 2e-16 ***
## L(ehatsq) 0.08640 0.01579 5.470 4.77e-08 ***
## L(ehatsq, k = -2) 0.03542 0.01587 2.232 0.0257 *
## L(ehatsq, k = -3) 0.07355 0.01585 4.641 3.58e-06 ***
## L(ehatsq, k = -4) 0.01887 0.01585 1.191 0.2339
## L(ehatsq, k = -5) 0.02656 0.01586 1.675 0.0940 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.958 on 3986 degrees of freedom
## Multiple R-squared: 0.01786, Adjusted R-squared: 0.01663
## F-statistic: 14.5 on 5 and 3986 DF, p-value: 4.187e-14
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market4.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -13.763, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -2557.8, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -9.6439, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -2627.7, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.255 0.826 0.309 0.00037 0.00037 0.00074 0.5 4.2e-07
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.05 -1.38 -1.26 -0.88 1256.70
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.442e+00 5.188e-01 2.779 0.00549 **
## data$seas_adj 3.954e-06 1.071e-05 0.369 0.71215
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26.28 on 2574 degrees of freedom
## Multiple R-squared: 5.29e-05, Adjusted R-squared: -0.0003356
## F-statistic: 0.1362 on 1 and 2574 DF, p-value: 0.7122
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8159 -1.0321 0.0355 1.1678 8.8222
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.722e+00 3.540e-02 -48.642 <2e-16 ***
## data$seas_adj 1.681e-06 7.312e-07 2.299 0.0216 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.794 on 2574 degrees of freedom
## Multiple R-squared: 0.002048, Adjusted R-squared: 0.001661
## F-statistic: 5.283 on 1 and 2574 DF, p-value: 0.02161## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 2576
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## 0.007917 -0.788530 -0.670571 -0.636377
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.569696 -0.498212 -0.459766 -0.246723
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.145027 -0.122145 -0.077508 -0.039707
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.110876 0.005154 0.098724 -0.025557
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## 0.044349 0.182202 -0.083089 -0.149910
## L(price, 9) L(price, 10)
## -0.089234 -0.065360
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 9253.459
## 2 9 10 9266.971
## 3 8 10 9274.667
## 4 7 10 9278.092
## 5 9 9 9291.753
## 6 8 9 9298.525
## 7 7 9 9302.019
## 8 6 10 9314.545
## 9 8 8 9314.801
## 10 7 8 9318.023
## 11 6 9 9337.221
## 12 7 7 9339.637
## 13 6 8 9353.387
## 14 6 7 9373.293
## 15 6 6 9402.344
## 16 5 10 9491.684
## 17 5 9 9514.715
## 18 5 8 9530.462
## 19 4 10 9545.357
## 20 5 7 9551.487
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 2576
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.5403 -0.7876 0.2310 0.9990 5.3464
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.007917 0.030181 0.262 0.793
## L(quantity, 1) -0.788530 0.019912 -39.600 < 2e-16 ***
## L(quantity, 2) -0.670571 0.025225 -26.583 < 2e-16 ***
## L(quantity, 3) -0.636377 0.028328 -22.465 < 2e-16 ***
## L(quantity, 4) -0.569696 0.030674 -18.573 < 2e-16 ***
## L(quantity, 5) -0.498212 0.031355 -15.890 < 2e-16 ***
## L(quantity, 6) -0.459766 0.031367 -14.658 < 2e-16 ***
## L(quantity, 7) -0.246723 0.030621 -8.057 1.20e-15 ***
## L(quantity, 8) -0.145027 0.028222 -5.139 2.98e-07 ***
## L(quantity, 9) -0.122145 0.025082 -4.870 1.19e-06 ***
## L(quantity, 10) -0.077508 0.019735 -3.927 8.82e-05 ***
## price -0.039707 0.100597 -0.395 0.693
## L(price, 1) -0.110876 0.100542 -1.103 0.270
## L(price, 2) 0.005154 0.100565 0.051 0.959
## L(price, 3) 0.098724 0.100539 0.982 0.326
## L(price, 4) -0.025557 0.100505 -0.254 0.799
## L(price, 5) 0.044349 0.100512 0.441 0.659
## L(price, 6) 0.182202 0.100502 1.813 0.070 .
## L(price, 7) -0.083089 0.100567 -0.826 0.409
## L(price, 8) -0.149910 0.100525 -1.491 0.136
## L(price, 9) -0.089234 0.100569 -0.887 0.375
## L(price, 10) -0.065360 0.098840 -0.661 0.509
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.514 on 2495 degrees of freedom
## (49 observations deleted due to missingness)
## Multiple R-squared: 0.4044, Adjusted R-squared: 0.3994
## F-statistic: 80.67 on 21 and 2495 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.451 -0.252 -0.224 -0.183 -0.139 -0.256 -0.107 -0.033 -0.048 -0.067 -0.003
## 12 13 14 15 16 17 18 19 20 21 22
## -0.045 -0.067 -0.081 -0.036 0.003 -0.007 -0.042 -0.036 -0.033 -0.057 0.059
## 23 24 25 26 27 28 29 30 31 32 33
## 0.018 0.025 0.011 0.028 -0.024 0.047 -0.085 -0.026 0.017 -0.019 -0.025
## 34
## -0.026## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.451 0.002 -0.054 0.004 0.008 -0.096 0.132 0.000 -0.029 -0.023
## 11 12 13 14 15 16 17 18 19 20 21
## 0.040 -0.041 -0.018 0.007 0.046 0.007 -0.030 -0.011 0.005 -0.006 -0.016
## 22 23 24 25 26 27 28 29 30 31 32
## 0.090 -0.056 0.011 -0.027 0.022 -0.038 0.046 -0.076 0.078 0.003 -0.035
## 33 34
## 0.009 -0.022
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7035 -0.5177 -0.4228 -0.2919 -0.1468 0.0001
## s.e. 0.0196 0.0234 0.0242 0.0234 0.0196 0.0103
##
## sigma^2 estimated as 2.575: log likelihood = -4871.88, aic = 9757.75
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 337.86, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 2570
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.286 -2.116 -1.544 0.164 64.584
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.94010 0.13888 13.969 < 2e-16 ***
## L(ehatsq) 0.07226 0.01938 3.728 0.000197 ***
## L(ehatsq, k = -2) 0.02951 0.01982 1.489 0.136731
## L(ehatsq, k = -3) 0.05922 0.01981 2.989 0.002830 **
## L(ehatsq, k = -4) 0.04138 0.01982 2.088 0.036926 *
## L(ehatsq, k = -5) 0.04039 0.01984 2.036 0.041862 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.869 on 2563 degrees of freedom
## Multiple R-squared: 0.01582, Adjusted R-squared: 0.0139
## F-statistic: 8.24 on 5 and 2563 DF, p-value: 9.857e-08
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market5.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -8.3133, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -2683, Truncation lag parameter = 10, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -8.4397, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -2845.7, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.242 0.786 0.308 1.5e-07 1.5e-07 3e-07 0.5 1.7e-08
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.088 -2.888 -2.108 0.322 73.771
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.344e+00 9.357e-02 35.736 <2e-16 ***
## data$seas_adj 1.090e-06 1.224e-06 0.891 0.373
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.818 on 3983 degrees of freedom
## Multiple R-squared: 0.0001991, Adjusted R-squared: -5.196e-05
## F-statistic: 0.793 on 1 and 3983 DF, p-value: 0.3732
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.8122 -0.9548 0.0336 1.1126 4.1589
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.863e-01 2.556e-02 7.290 3.71e-13 ***
## data$seas_adj 3.383e-07 3.343e-07 1.012 0.312
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.589 on 3983 degrees of freedom
## Multiple R-squared: 0.0002571, Adjusted R-squared: 6.141e-06
## F-statistic: 1.024 on 1 and 3983 DF, p-value: 0.3115## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3975
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## -0.006668 -0.790404 -0.643407 -0.535715
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.471064 -0.401057 -0.352358 -0.281675
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.220669 -0.181192 -0.091519 -0.037319
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.066410 0.262314 0.332898 -0.016295
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## -0.363815 -0.331858 0.158690 0.283942
## L(price, 9) L(price, 10)
## 0.123771 -0.053904
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 9362.662
## 2 9 10 9383.068
## 3 9 9 9398.048
## 4 8 10 9413.465
## 5 7 10 9428.205
## 6 8 9 9428.333
## 7 7 9 9443.183
## 8 8 8 9447.952
## 9 6 10 9457.380
## 10 7 8 9462.637
## 11 6 9 9472.649
## 12 7 7 9480.985
## 13 6 8 9492.357
## 14 5 10 9501.099
## 15 6 7 9510.515
## 16 5 9 9517.129
## 17 6 6 9532.264
## 18 5 8 9536.832
## 19 4 10 9543.410
## 20 5 7 9554.949
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3975
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.7411 -0.7577 0.1585 0.9511 4.0302
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.006668 0.026991 -0.247 0.8049
## L(quantity, 1) -0.790404 0.019373 -40.800 < 2e-16 ***
## L(quantity, 2) -0.643407 0.024503 -26.258 < 2e-16 ***
## L(quantity, 3) -0.535715 0.027206 -19.691 < 2e-16 ***
## L(quantity, 4) -0.471064 0.028618 -16.461 < 2e-16 ***
## L(quantity, 5) -0.401057 0.029255 -13.709 < 2e-16 ***
## L(quantity, 6) -0.352358 0.029225 -12.057 < 2e-16 ***
## L(quantity, 7) -0.281675 0.028509 -9.880 < 2e-16 ***
## L(quantity, 8) -0.220669 0.027077 -8.150 5.57e-16 ***
## L(quantity, 9) -0.181192 0.024460 -7.408 1.72e-13 ***
## L(quantity, 10) -0.091519 0.019374 -4.724 2.44e-06 ***
## price -0.037319 0.151221 -0.247 0.8051
## L(price, 1) -0.066410 0.155590 -0.427 0.6695
## L(price, 2) 0.262314 0.157130 1.669 0.0952 .
## L(price, 3) 0.332898 0.156241 2.131 0.0332 *
## L(price, 4) -0.016295 0.164433 -0.099 0.9211
## L(price, 5) -0.363815 0.163950 -2.219 0.0266 *
## L(price, 6) -0.331858 0.169897 -1.953 0.0509 .
## L(price, 7) 0.158690 0.188120 0.844 0.3990
## L(price, 8) 0.283942 0.190133 1.493 0.1355
## L(price, 9) 0.123771 0.191979 0.645 0.5192
## L(price, 10) -0.053904 0.185840 -0.290 0.7718
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.392 on 2647 degrees of freedom
## (1108 observations deleted due to missingness)
## Multiple R-squared: 0.3911, Adjusted R-squared: 0.3863
## F-statistic: 80.96 on 21 and 2647 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.472 -0.296 -0.209 -0.183 -0.127 -0.131 -0.111 -0.084 -0.090 -0.099 -0.078
## 12 13 14 15 16 17 18 19 20 21 22
## -0.067 -0.056 -0.088 -0.007 -0.043 -0.056 -0.042 -0.030 -0.038 -0.048 -0.037
## 23 24 25 26 27 28 29 30 31 32 33
## 0.012 -0.008 -0.027 -0.051 -0.004 -0.016 -0.037 -0.016 0.012 0.008 0.002
## 34 35 36
## 0.003 0.002 -0.006## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.472 -0.007 -0.004 -0.020 0.022 -0.026 0.010 0.008 -0.015 -0.005
## 11 12 13 14 15 16 17 18 19 20 21
## 0.014 -0.002 0.003 -0.025 0.060 -0.052 0.003 0.014 0.000 -0.006 -0.007
## 22 23 24 25 26 27 28 29 30 31 32
## 0.012 0.026 -0.033 -0.004 -0.006 0.035 -0.023 -0.011 0.025 0.003 -0.012
## 33 34 35 36
## -0.003 0.003 -0.002 -0.006
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7357 -0.5440 -0.3958 -0.2736 -0.1267 -0.0004
## s.e. 0.0157 0.0191 0.0200 0.0191 0.0157 0.0074
##
## sigma^2 estimated as 2.044: log likelihood = -7077.72, aic = 14169.45
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 690.73, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3979
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.825 -1.795 -1.214 0.280 90.821
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.7948675 0.0961361 18.670 < 2e-16 ***
## L(ehatsq) 0.0683858 0.0158264 4.321 1.59e-05 ***
## L(ehatsq, k = -2) 0.0324312 0.0158670 2.044 0.041 *
## L(ehatsq, k = -3) 0.0004644 0.0159046 0.029 0.977
## L(ehatsq, k = -4) 0.0164164 0.0159023 1.032 0.302
## L(ehatsq, k = -5) 0.0044875 0.0158718 0.283 0.777
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.288 on 3972 degrees of freedom
## Multiple R-squared: 0.006125, Adjusted R-squared: 0.004874
## F-statistic: 4.895 on 5 and 3972 DF, p-value: 0.000181
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market6.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -5.1694, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -4175.7, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -11.253, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -4162.5, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.270 0.800 0.338 5.6e-06 5.6e-06 1.1e-05 0.5 1.3e-07
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0207 -0.0201 -0.0181 -0.0125 3.2272
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.073e-02 1.980e-03 10.470 <2e-16 ***
## data$seas_adj -5.851e-09 5.477e-08 -0.107 0.915
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1177 on 3625 degrees of freedom
## Multiple R-squared: 3.149e-06, Adjusted R-squared: -0.0002727
## F-statistic: 0.01141 on 1 and 3625 DF, p-value: 0.9149
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.0606 -1.2968 0.0742 1.2290 7.2264
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.048e+00 3.289e-02 -183.885 <2e-16 ***
## data$seas_adj 1.626e-06 9.098e-07 1.787 0.074 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.955 on 3625 degrees of freedom
## Multiple R-squared: 0.0008801, Adjusted R-squared: 0.0006045
## F-statistic: 3.193 on 1 and 3625 DF, p-value: 0.07403## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3627
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## -0.0002696 -0.8344050 -0.7705502 -0.6843870
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.5783322 -0.4792760 -0.3597994 -0.1940630
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.1114287 -0.0673050 -0.0934059 -0.1698720
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.0405283 -0.1301565 -0.1083398 -0.0460961
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## -0.1400410 -0.0746170 0.1440679 0.1975439
## L(price, 9) L(price, 10)
## 0.0580031 0.1453591
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 8631.466
## 2 8 10 8646.680
## 3 9 10 8648.386
## 4 7 10 8649.777
## 5 6 10 8668.466
## 6 8 9 8687.697
## 7 9 9 8689.415
## 8 7 9 8691.014
## 9 6 9 8709.907
## 10 8 8 8723.370
## 11 7 8 8727.147
## 12 6 8 8745.948
## 13 5 10 8753.312
## 14 7 7 8782.401
## 15 5 9 8794.630
## 16 6 7 8800.948
## 17 4 10 8829.792
## 18 5 8 8831.479
## 19 6 6 8847.163
## 20 4 9 8871.961
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3627
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.8320 -1.0450 -0.0196 1.1135 7.6989
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0002696 0.0380568 -0.007 0.994348
## L(quantity, 1) -0.8344050 0.0215393 -38.739 < 2e-16 ***
## L(quantity, 2) -0.7705502 0.0280993 -27.422 < 2e-16 ***
## L(quantity, 3) -0.6843870 0.0325738 -21.010 < 2e-16 ***
## L(quantity, 4) -0.5783322 0.0355502 -16.268 < 2e-16 ***
## L(quantity, 5) -0.4792760 0.0370221 -12.946 < 2e-16 ***
## L(quantity, 6) -0.3597994 0.0371405 -9.688 < 2e-16 ***
## L(quantity, 7) -0.1940630 0.0358069 -5.420 6.64e-08 ***
## L(quantity, 8) -0.1114287 0.0327648 -3.401 0.000684 ***
## L(quantity, 9) -0.0673050 0.0282267 -2.384 0.017191 *
## L(quantity, 10) -0.0934059 0.0215372 -4.337 1.51e-05 ***
## price -0.1698720 0.0628119 -2.704 0.006896 **
## L(price, 1) -0.0405283 0.0688629 -0.589 0.556234
## L(price, 2) -0.1301565 0.0805078 -1.617 0.106092
## L(price, 3) -0.1083398 0.0842780 -1.286 0.198755
## L(price, 4) -0.0460961 0.0877739 -0.525 0.599521
## L(price, 5) -0.1400410 0.0870334 -1.609 0.107753
## L(price, 6) -0.0746170 0.0858024 -0.870 0.384596
## L(price, 7) 0.1440679 0.0825351 1.746 0.081035 .
## L(price, 8) 0.1975439 0.0785671 2.514 0.011999 *
## L(price, 9) 0.0580031 0.0705444 0.822 0.411043
## L(price, 10) 0.1453591 0.0630931 2.304 0.021324 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.77 on 2141 degrees of freedom
## (747 observations deleted due to missingness)
## Multiple R-squared: 0.4299, Adjusted R-squared: 0.4244
## F-statistic: 76.89 on 21 and 2141 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.462 -0.333 -0.258 -0.201 -0.178 -0.194 -0.082 -0.062 -0.002 -0.108 -0.076
## 12 13 14 15 16 17 18 19 20 21 22
## -0.077 -0.075 -0.049 -0.064 -0.095 -0.019 -0.007 -0.021 -0.069 -0.106 -0.036
## 23 24 25 26 27 28 29 30 31 32 33
## -0.010 -0.023 0.014 -0.047 -0.073 -0.055 -0.014 -0.015 -0.017 -0.009 -0.046
## 34 35
## -0.041 -0.035## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.462 -0.049 0.003 0.009 -0.008 -0.021 0.073 -0.032 0.018 -0.086
## 11 12 13 14 15 16 17 18 19 20 21
## 0.060 -0.006 -0.002 0.018 -0.021 -0.013 0.045 -0.014 -0.021 -0.013 -0.002
## 22 23 24 25 26 27 28 29 30 31 32
## 0.055 -0.016 -0.018 0.025 -0.050 -0.002 0.034 0.027 -0.023 -0.007 -0.002
## 33 34 35
## -0.026 0.026 0.005
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7883 -0.6608 -0.5034 -0.3352 -0.1781 0.0007
## s.e. 0.0163 0.0202 0.0214 0.0202 0.0164 0.0087
##
## sigma^2 estimated as 3.289: log likelihood = -7304.24, aic = 14622.48
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 402.65, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3621
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.677 -2.810 -2.038 0.567 153.113
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.682855 0.151256 17.737 < 2e-16 ***
## L(ehatsq) 0.054049 0.016616 3.253 0.001153 **
## L(ehatsq, k = -2) 0.058132 0.016613 3.499 0.000472 ***
## L(ehatsq, k = -3) 0.008744 0.016651 0.525 0.599515
## L(ehatsq, k = -4) 0.042333 0.016640 2.544 0.010998 *
## L(ehatsq, k = -5) 0.022488 0.016650 1.351 0.176893
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.153 on 3614 degrees of freedom
## Multiple R-squared: 0.009739, Adjusted R-squared: 0.008369
## F-statistic: 7.109 on 5 and 3614 DF, p-value: 1.26e-06
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market7.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -7.6501, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -4113.5, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -15.496, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -3871.1, Truncation lag parameter = 9, p-value
## = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.203 0.699 0.291 2e-05 2e-05 4e-05 0.5 1.2e-07
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -405.20 0.82 0.85 0.85 2829.97
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.498e-01 7.736e-01 -1.099 0.272
## data$seas_adj 2.265e-04 1.151e-05 19.681 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.75 on 3869 degrees of freedom
## Multiple R-squared: 0.09101, Adjusted R-squared: 0.09077
## F-statistic: 387.4 on 1 and 3869 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.7662 -1.9218 -0.6505 1.7633 9.1490
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.544e+00 4.463e-02 -124.226 < 2e-16 ***
## data$seas_adj 4.305e-06 6.639e-07 6.484 1.01e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.755 on 3869 degrees of freedom
## Multiple R-squared: 0.01075, Adjusted R-squared: 0.01049
## F-statistic: 42.04 on 1 and 3869 DF, p-value: 1.006e-10## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3862
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3) L(quantity, 4)
## -0.008818 -0.843245 -0.703392 -0.653581 -0.633469
## L(quantity, 5) L(quantity, 6) L(quantity, 7) L(quantity, 8) L(quantity, 9)
## -0.585256 -0.440221 -0.013479 0.050573 -0.039564
## price L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.064244 0.037691 -0.244031 -0.157243 -0.078888
## L(price, 5) L(price, 6) L(price, 7) L(price, 8) L(price, 9)
## 0.021942 0.190064 0.195730 0.111009 -0.040175
## L(price, 10)
## 0.127802
##
##
## $best_order
## quantity price
## 9 10
##
## $top_orders
## quantity price AIC
## 1 9 10 13375.14
## 2 10 10 13377.14
## 3 8 10 13378.29
## 4 7 10 13399.76
## 5 6 10 13408.64
## 6 9 9 13413.75
## 7 8 9 13416.99
## 8 7 9 13438.53
## 9 8 8 13442.15
## 10 6 9 13448.56
## 11 7 8 13463.64
## 12 6 8 13473.64
## 13 7 7 13493.17
## 14 6 7 13503.09
## 15 6 6 13530.45
## 16 5 10 14074.19
## 17 5 9 14103.70
## 18 5 8 14138.47
## 19 5 7 14165.96
## 20 5 6 14195.55
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 3862
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.3034 -1.0043 -0.0366 0.8526 8.6004
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.008818 0.032940 -0.268 0.7889
## L(quantity, 1) -0.843245 0.017529 -48.106 <2e-16 ***
## L(quantity, 2) -0.703392 0.022911 -30.701 <2e-16 ***
## L(quantity, 3) -0.653581 0.026002 -25.136 <2e-16 ***
## L(quantity, 4) -0.633469 0.027347 -23.164 <2e-16 ***
## L(quantity, 5) -0.585256 0.027702 -21.127 <2e-16 ***
## L(quantity, 6) -0.440221 0.027384 -16.076 <2e-16 ***
## L(quantity, 7) -0.013479 0.026057 -0.517 0.6050
## L(quantity, 8) 0.050573 0.022903 2.208 0.0273 *
## L(quantity, 9) -0.039564 0.017477 -2.264 0.0237 *
## price -0.064244 0.152833 -0.420 0.6743
## L(price, 1) 0.037691 0.156704 0.241 0.8099
## L(price, 2) -0.244031 0.157336 -1.551 0.1210
## L(price, 3) -0.157243 0.171537 -0.917 0.3594
## L(price, 4) -0.078888 0.177166 -0.445 0.6562
## L(price, 5) 0.021942 0.176354 0.124 0.9010
## L(price, 6) 0.190064 0.170092 1.117 0.2639
## L(price, 7) 0.195730 0.153787 1.273 0.2032
## L(price, 8) 0.111009 0.152834 0.726 0.4677
## L(price, 9) -0.040175 0.152396 -0.264 0.7921
## L(price, 10) 0.127802 0.151170 0.845 0.3979
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.878 on 3237 degrees of freedom
## (344 observations deleted due to missingness)
## Multiple R-squared: 0.4898, Adjusted R-squared: 0.4866
## F-statistic: 155.4 on 20 and 3237 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.429 -0.261 -0.196 -0.199 -0.267 -0.418 -0.034 0.100 -0.047 -0.021 -0.090
## 12 13 14 15 16 17 18 19 20 21 22
## -0.165 -0.253 -0.030 0.026 0.002 -0.025 0.063 -0.033 -0.047 0.008 -0.005
## 23 24 25 26 27 28 29 30 31 32 33
## -0.004 0.013 -0.060 -0.047 -0.033 -0.035 0.027 0.001 -0.081 0.095 -0.029
## 34 35
## -0.029 0.012## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.429 -0.029 -0.022 -0.038 -0.059 -0.077 0.315 -0.046 -0.132 0.048
## 11 12 13 14 15 16 17 18 19 20 21
## -0.078 -0.053 -0.022 0.267 -0.043 -0.093 0.004 0.004 -0.128 0.049 0.166
## 22 23 24 25 26 27 28 29 30 31 32
## -0.028 -0.066 0.009 -0.062 -0.041 0.035 0.128 0.010 -0.079 -0.027 0.070
## 33 34 35
## -0.173 0.098 0.098
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.6836 -0.5233 -0.4311 -0.3679 -0.2672 0.0015
## s.e. 0.0155 0.0181 0.0187 0.0181 0.0155 0.0101
##
## sigma^2 estimated as 4.26: log likelihood = -8296.35, aic = 16606.7
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 411.55, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 3865
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26.518 -3.318 -2.186 0.810 159.327
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.89458 0.17031 16.996 < 2e-16 ***
## L(ehatsq) 0.13318 0.01605 8.298 < 2e-16 ***
## L(ehatsq, k = -2) 0.10326 0.01607 6.424 1.49e-10 ***
## L(ehatsq, k = -3) 0.03251 0.01620 2.007 0.0448 *
## L(ehatsq, k = -4) 0.01124 0.01622 0.693 0.4881
## L(ehatsq, k = -5) 0.04156 0.01626 2.556 0.0106 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.141 on 3858 degrees of freedom
## Multiple R-squared: 0.03776, Adjusted R-squared: 0.03652
## F-statistic: 30.28 on 5 and 3858 DF, p-value: < 2.2e-16
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Market9.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -12.185, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -2314.2, Truncation lag parameter = 8, p-value
## = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -10.863, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -2961.4, Truncation lag parameter = 8, p-value
## = 0.01
## alternative hypothesis: stationary## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.259 0.779 0.332 1.4e-06 1.4e-06 2.7e-06 0.5 5e-08
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.14361 -0.01644 -0.01597 -0.01397 1.45242
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.661e-02 1.623e-03 10.234 < 2e-16 ***
## data$seas_adj 2.119e-07 3.543e-08 5.978 2.57e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08083 on 2513 degrees of freedom
## Multiple R-squared: 0.01402, Adjusted R-squared: 0.01363
## F-statistic: 35.74 on 1 and 2513 DF, p-value: 2.572e-09
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.1412 -1.2812 -0.1547 1.0865 7.2997
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.915e+00 4.201e-02 -164.601 < 2e-16 ***
## data$seas_adj 6.258e-06 9.174e-07 6.821 1.13e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.092 on 2513 degrees of freedom
## Multiple R-squared: 0.01818, Adjusted R-squared: 0.01779
## F-statistic: 46.53 on 1 and 2513 DF, p-value: 1.125e-11## Warning in log(x6): NaNs produced
## $best_model
##
## Time series regression with "zooreg" data:
## Start = 12, End = 2515
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3) L(quantity, 4)
## 0.0004413 -0.7657515 -0.5947707 -0.4952793 -0.3632658
## L(quantity, 5) L(quantity, 6) L(quantity, 7) L(quantity, 8) L(quantity, 9)
## -0.3190098 -0.2612074 -0.1545968 -0.1271984 -0.0324305
## price L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.0077796 -0.1948654 -0.3257191 -0.1010545 0.1860741
## L(price, 5) L(price, 6) L(price, 7) L(price, 8) L(price, 9)
## 0.0101725 0.2660725 0.2328208 0.2640935 0.2945873
## L(price, 10)
## 0.2847967
##
##
## $best_order
## quantity price
## 9 10
##
## $top_orders
## quantity price AIC
## 1 9 10 9504.339
## 2 8 10 9504.856
## 3 10 10 9505.495
## 4 7 10 9527.720
## 5 9 9 9528.162
## 6 8 9 9529.141
## 7 6 10 9533.600
## 8 8 8 9552.637
## 9 7 9 9554.673
## 10 6 9 9558.692
## 11 7 8 9577.502
## 12 5 10 9580.392
## 13 6 8 9581.272
## 14 7 7 9590.529
## 15 6 7 9594.267
## 16 5 9 9603.360
## 17 6 6 9607.166
## 18 4 10 9614.711
## 19 5 8 9626.259
## 20 5 7 9639.753
##
##
## Time series regression with "zooreg" data:
## Start = 12, End = 2515
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.4156 -0.9626 0.0844 0.8734 8.2934
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0004413 0.0388967 0.011 0.990949
## L(quantity, 1) -0.7657515 0.0208173 -36.784 < 2e-16 ***
## L(quantity, 2) -0.5947707 0.0260205 -22.858 < 2e-16 ***
## L(quantity, 3) -0.4952793 0.0285752 -17.332 < 2e-16 ***
## L(quantity, 4) -0.3632658 0.0298746 -12.160 < 2e-16 ***
## L(quantity, 5) -0.3190098 0.0300256 -10.625 < 2e-16 ***
## L(quantity, 6) -0.2612074 0.0298395 -8.754 < 2e-16 ***
## L(quantity, 7) -0.1545968 0.0285384 -5.417 6.69e-08 ***
## L(quantity, 8) -0.1271984 0.0259191 -4.908 9.87e-07 ***
## L(quantity, 9) -0.0324305 0.0205299 -1.580 0.114319
## price -0.0077796 0.0814788 -0.095 0.923942
## L(price, 1) -0.1948654 0.0922513 -2.112 0.034766 *
## L(price, 2) -0.3257191 0.0956500 -3.405 0.000672 ***
## L(price, 3) -0.1010545 0.0964779 -1.047 0.295009
## L(price, 4) 0.1860741 0.0933607 1.993 0.046372 *
## L(price, 5) 0.0101725 0.0935065 0.109 0.913380
## L(price, 6) 0.2660725 0.0944174 2.818 0.004873 **
## L(price, 7) 0.2328208 0.0980850 2.374 0.017694 *
## L(price, 8) 0.2640935 0.0977485 2.702 0.006948 **
## L(price, 9) 0.2945873 0.0948351 3.106 0.001918 **
## L(price, 10) 0.2847967 0.0842907 3.379 0.000740 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.872 on 2296 degrees of freedom
## (188 observations deleted due to missingness)
## Multiple R-squared: 0.3885, Adjusted R-squared: 0.3832
## F-statistic: 72.94 on 20 and 2296 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.476 -0.290 -0.231 -0.120 -0.126 -0.143 -0.040 -0.096 -0.039 -0.025 -0.004
## 12 13 14 15 16 17 18 19 20 21 22
## -0.067 -0.111 -0.013 0.014 -0.076 -0.065 -0.031 -0.022 -0.122 0.007 -0.004
## 23 24 25 26 27 28 29 30 31 32 33
## -0.031 0.027 -0.048 -0.034 0.008 0.006 -0.034 -0.043 -0.017 0.007 -0.026
## 34
## -0.019## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.476 0.003 -0.027 0.047 -0.047 -0.014 0.066 -0.071 0.050 -0.014
## 11 12 13 14 15 16 17 18 19 20 21
## 0.014 -0.057 -0.001 0.074 -0.022 -0.061 0.034 0.024 -0.018 -0.064 0.121
## 22 23 24 25 26 27 28 29 30 31 32
## -0.061 -0.010 0.046 -0.059 0.017 0.020 0.015 -0.053 0.015 0.024 0.007
## 33 34
## -0.037 0.009
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7278 -0.5303 -0.3802 -0.2137 -0.1297 0.0018
## s.e. 0.0198 0.0243 0.0254 0.0243 0.0199 0.0130
##
## sigma^2 estimated as 3.797: log likelihood = -5244.53, aic = 10503.07
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 447.61, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 2509
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.281 -2.803 -2.133 -0.440 82.064
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.315974 0.210114 11.022 < 2e-16 ***
## L(ehatsq) 0.207889 0.019408 10.712 < 2e-16 ***
## L(ehatsq, k = -2) 0.107728 0.020288 5.310 1.19e-07 ***
## L(ehatsq, k = -3) 0.062018 0.020597 3.011 0.00263 **
## L(ehatsq, k = -4) 0.016905 0.020630 0.819 0.41262
## L(ehatsq, k = -5) -0.002132 0.020252 -0.105 0.91617
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.056 on 2502 degrees of freedom
## Multiple R-squared: 0.06811, Adjusted R-squared: 0.06624
## F-statistic: 36.57 on 5 and 2502 DF, p-value: < 2.2e-16
final_function("D:/DipankarSir/DipankarSir/dataanalysis_/Marketwb.csv")## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Missing values detected. To allow DSA to work properly, missing values are imputed using the 'last observation carried forward' algorithm (zoo::na.locf). Leading NAs are removed.
## You might want to impute the series outside of this function.##
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|======================================================================| 100%## Warning in adf.test(data$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$seas_adj
## Dickey-Fuller = -11.331, Lag order = 16, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(data$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: data$seas_adj
## Dickey-Fuller Z(alpha) = -2733.4, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary## Warning in adf.test(quantity$seas_adj): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: quantity$seas_adj
## Dickey-Fuller = -6.5987, Lag order = 16, p-value = 0.01
## alternative hypothesis: stationary## Warning in pp.test(quantity$seas_adj): p-value smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: quantity$seas_adj
## Dickey-Fuller Z(alpha) = -2907.3, Truncation lag parameter = 10,
## p-value = 0.01
## alternative hypothesis: stationary
## # A tibble: 1 × 9
## sumA sumAB collusionmeasure1 varA varB varAplusB varratio varAB
## <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 0.611 0.787 0.776 3.4e-08 4e-08 7.4e-08 0.46 2e-09
## # ℹ 1 more variable: collusionmeasure2 <dbl>
##
## Call:
## lm(formula = quantity$seas_adj ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.676 -3.477 -2.740 -1.015 155.145
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.882558 0.148631 26.122 < 2e-16 ***
## data$seas_adj 0.008930 0.002667 3.348 0.00082 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.934 on 4211 degrees of freedom
## Multiple R-squared: 0.002655, Adjusted R-squared: 0.002418
## F-statistic: 11.21 on 1 and 4211 DF, p-value: 0.0008202
##
##
## Call:
## lm(formula = log(quantity$seas_adj) ~ data$seas_adj)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.1325 -0.8744 -0.0079 0.8408 4.8014
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2259081 0.0254403 8.880 < 2e-16 ***
## data$seas_adj 0.0020731 0.0004565 4.541 5.75e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.529 on 4211 degrees of freedom
## Multiple R-squared: 0.004874, Adjusted R-squared: 0.004637
## F-statistic: 20.62 on 1 and 4211 DF, p-value: 5.745e-06
##
## $best_model
##
## Time series regression with "ts" data:
## Start = 12, End = 4213
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Coefficients:
## (Intercept) L(quantity, 1) L(quantity, 2) L(quantity, 3)
## -0.00357 -0.76453 -0.61442 -0.49434
## L(quantity, 4) L(quantity, 5) L(quantity, 6) L(quantity, 7)
## -0.41705 -0.36631 -0.33225 -0.28288
## L(quantity, 8) L(quantity, 9) L(quantity, 10) price
## -0.22535 -0.13269 -0.07577 0.07466
## L(price, 1) L(price, 2) L(price, 3) L(price, 4)
## -0.08096 -0.82585 0.40747 -0.52027
## L(price, 5) L(price, 6) L(price, 7) L(price, 8)
## -0.58606 -0.34992 -0.05045 -0.15107
## L(price, 9) L(price, 10)
## 0.42956 0.61028
##
##
## $best_order
## quantity price
## 10 10
##
## $top_orders
## quantity price AIC
## 1 10 10 14128.28
## 2 9 10 14150.48
## 3 9 9 14153.55
## 4 8 2 14167.58
## 5 8 1 14168.12
## 6 8 3 14168.62
## 7 8 4 14170.03
## 8 8 5 14171.37
## 9 8 6 14173.09
## 10 8 7 14175.09
## 11 8 8 14176.98
## 12 7 2 14233.26
## 13 7 1 14233.90
## 14 7 3 14234.26
## 15 7 4 14235.96
## 16 7 5 14237.15
## 17 7 6 14238.93
## 18 7 7 14240.92
## 19 6 10 14286.16
## 20 6 9 14289.72
##
##
## Time series regression with "ts" data:
## Start = 12, End = 4213
##
## Call:
## dynlm::dynlm(formula = full_formula, data = data, start = start,
## end = end)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.9668 -0.6233 0.2033 0.8309 4.6228
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.00357 0.01999 -0.179 0.858
## L(quantity, 1) -0.76453 0.01542 -49.587 < 2e-16 ***
## L(quantity, 2) -0.61442 0.01931 -31.811 < 2e-16 ***
## L(quantity, 3) -0.49434 0.02124 -23.275 < 2e-16 ***
## L(quantity, 4) -0.41705 0.02214 -18.835 < 2e-16 ***
## L(quantity, 5) -0.36631 0.02248 -16.293 < 2e-16 ***
## L(quantity, 6) -0.33225 0.02248 -14.779 < 2e-16 ***
## L(quantity, 7) -0.28288 0.02214 -12.777 < 2e-16 ***
## L(quantity, 8) -0.22535 0.02123 -10.616 < 2e-16 ***
## L(quantity, 9) -0.13269 0.01931 -6.872 7.27e-12 ***
## L(quantity, 10) -0.07577 0.01542 -4.914 9.26e-07 ***
## price 0.07466 0.53333 0.140 0.889
## L(price, 1) -0.08096 0.53866 -0.150 0.881
## L(price, 2) -0.82585 0.53835 -1.534 0.125
## L(price, 3) 0.40747 0.53852 0.757 0.449
## L(price, 4) -0.52027 0.53860 -0.966 0.334
## L(price, 5) -0.58606 0.53856 -1.088 0.277
## L(price, 6) -0.34992 0.53864 -0.650 0.516
## L(price, 7) -0.05044 0.53835 -0.094 0.925
## L(price, 8) -0.15107 0.53821 -0.281 0.779
## L(price, 9) 0.42956 0.53821 0.798 0.425
## L(price, 10) 0.61028 0.53108 1.149 0.251
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.296 on 4180 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.3734, Adjusted R-squared: 0.3703
## F-statistic: 118.6 on 21 and 4180 DF, p-value: < 2.2e-16## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter
##
## Partial autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.466 -0.297 -0.199 -0.145 -0.117 -0.117 -0.112 -0.124 -0.075 -0.075 -0.070
## 12 13 14 15 16 17 18 19 20 21 22
## -0.090 -0.081 -0.031 -0.060 -0.078 -0.039 -0.020 -0.046 -0.016 -0.024 0.010
## 23 24 25 26 27 28 29 30 31 32 33
## -0.030 -0.070 -0.077 -0.070 -0.079 -0.071 -0.092 -0.046 -0.060 -0.029 0.004
## 34 35 36
## -0.004 0.023 0.007## Warning in plot.window(...): "title" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "title" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "title" is not a
## graphical parameter## Warning in box(...): "title" is not a graphical parameter## Warning in title(...): "title" is not a graphical parameter##
## Autocorrelations of series 'na.omit(new_df$quantity)', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.466 -0.016 0.006 -0.004 -0.007 -0.015 -0.002 -0.012 0.032 -0.019
## 11 12 13 14 15 16 17 18 19 20 21
## 0.002 -0.014 0.011 0.028 -0.037 -0.002 0.031 -0.002 -0.025 0.027 -0.017
## 22 23 24 25 26 27 28 29 30 31 32
## 0.023 -0.036 -0.014 0.011 0.008 -0.006 0.008 -0.013 0.037 -0.021 0.017
## 33 34 35 36
## 0.007 -0.016 0.017 -0.023
##
## Call:
## arima(x = na.omit(new_df$quantity), order = c(5, 0, 0))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 intercept
## -0.7085 -0.5120 -0.3505 -0.2254 -0.1170 -9e-04
## s.e. 0.0153 0.0185 0.0194 0.0185 0.0153 7e-03
##
## sigma^2 estimated as 1.766: log likelihood = -7174.58, aic = 14363.17
##
## Training set error measures:## Warning in trainingaccuracy(object, test, d, D): test elements must be within
## sample
## ME RMSE MAE MPE MAPE
## Training set NaN NaN NaN NaN NaN
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: quantity_diff
## Chi-squared = 557.7, df = 5, p-value < 2.2e-16
##
##
## Time series regression with "ts" data:
## Start = 2, End = 4207
##
## Call:
## dynlm(formula = ehatsq ~ L(ehatsq) + L(ehatsq, k = -2) + L(ehatsq,
## k = -3) + L(ehatsq, k = -4) + L(ehatsq, k = -5), data = ehatsq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.516 -1.534 -1.122 0.036 60.606
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.485611 0.080822 18.381 < 2e-16 ***
## L(ehatsq) 0.048064 0.015400 3.121 0.00181 **
## L(ehatsq, k = -2) 0.041418 0.015425 2.685 0.00728 **
## L(ehatsq, k = -3) 0.026571 0.015431 1.722 0.08517 .
## L(ehatsq, k = -4) 0.007893 0.015441 0.511 0.60928
## L(ehatsq, k = -5) 0.035668 0.015421 2.313 0.02077 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.738 on 4200 degrees of freedom
## Multiple R-squared: 0.006697, Adjusted R-squared: 0.005515
## F-statistic: 5.664 on 5 and 4200 DF, p-value: 3.277e-05