Rest of Mock/Sample
- Direct download:
- Download data on UK unemployment, CPI inflation and GDP growth from the Fred website using the
quantmodpackage.
- Download data on UK unemployment, CPI inflation and GDP growth from the Fred website using the
library(quantmod)
getSymbols("GBRCPIALLMINMEI",src="FRED",return.class="zoo") # CPI since 1955 (from FRED)## [1] "GBRCPIALLMINMEI"#need inflation not CPI
infl <- diff(log(GBRCPIALLMINMEI),lag=12,differences=1)
getSymbols("LMUNRRTTGBM156S",src="FRED",return.class="zoo") # unemployment since 1955, SA (unfortunately)## [1] "LMUNRRTTGBM156S"getSymbols("UKNGDP",src="FRED",return.class="zoo") # nominal GDP (from FRED)## [1] "UKNGDP"#need GDP growth not GDP
gdp.g <- diff(log(UKNGDP),lag=4,differences=1)b. Combine the data into a data frame, and create lags of inflation and GDP growth.#combination involves first making monthly data quarterly. We need aggregate() for this.
#a) need first to create variable to aggregate using
infl.yq <- as.numeric(format(index(infl),"%Y"))+0.25*(as.numeric(format(index(infl),"%m"))/12>0.25)+0.25*(as.numeric(format(index(infl),"%m"))/12>0.5)+0.25*(as.numeric(format(index(infl),"%m"))/12>0.75)
LMUNRRTTGBM156S.yq <- as.numeric(format(index(LMUNRRTTGBM156S),"%Y"))+0.25*(as.numeric(format(index(LMUNRRTTGBM156S),"%m"))/12>0.25)+0.25*(as.numeric(format(index(LMUNRRTTGBM156S),"%m"))/12>0.5)+0.25*(as.numeric(format(index(LMUNRRTTGBM156S),"%m"))/12>0.75)
#b) next to aggregate it taking mean value for month
infl.q <- aggregate(infl,by=list(infl.yq),FUN=mean,freq=4)
unr.q <- aggregate(LMUNRRTTGBM156S,by=list(LMUNRRTTGBM156S.yq),FUN=mean)
data.f <- data.frame("date"=seq(1956,2014.75,0.25),
"gdp.g"=as.numeric(coredata(gdp.g)),"gdp.g.1"=as.numeric(lag(gdp.g,k=-1,na.pad=T)),
"unr"=unr.q[5:NROW(unr.q)],"unr.1"=as.numeric(lag(unr.q[5:NROW(unr.q)],k=-1,na.pad=T)),
"infl"=infl.q,"infl.1"=as.numeric(lag(infl.q,k=-1,na.pad=T)))
str(data.f)## 'data.frame': 236 obs. of 7 variables:
## $ date : num 1956 1956 1956 1957 1957 ...
## $ gdp.g : num 0.0833 0.092 0.0729 0.0787 0.0551 ...
## $ gdp.g.1: num NA 0.0833 0.092 0.0729 0.0787 ...
## $ unr : num 1.07 1.1 1.2 1.23 1.47 ...
## $ unr.1 : num NA 1.07 1.1 1.2 1.23 ...
## $ infl : num 0.0539 0.0635 0.0456 0.032 0.0375 ...
## $ infl.1 : num NA 0.0539 0.0635 0.0456 0.032 ...summary(data.f)## date gdp.g gdp.g.1 unr
## Min. :1956 Min. :-0.04316 Min. :-0.04316 Min. : 1.067
## 1st Qu.:1971 1st Qu.: 0.04824 1st Qu.: 0.04830 1st Qu.: 2.400
## Median :1985 Median : 0.06452 Median : 0.06456 Median : 3.550
## Mean :1985 Mean : 0.07677 Mean : 0.07694 Mean : 4.452
## 3rd Qu.:2000 3rd Qu.: 0.09763 3rd Qu.: 0.09777 3rd Qu.: 5.917
## Max. :2015 Max. : 0.23333 Max. : 0.23333 Max. :10.567
## NA's :1
## unr.1 infl infl.1
## Min. : 1.067 Min. :-0.004542 Min. :-0.004542
## 1st Qu.: 2.400 1st Qu.: 0.020723 1st Qu.: 0.020732
## Median : 3.600 Median : 0.037324 Median : 0.037385
## Mean : 4.460 Mean : 0.050378 Mean : 0.050554
## 3rd Qu.: 5.933 3rd Qu.: 0.060556 3rd Qu.: 0.060746
## Max. :10.567 Max. : 0.235589 Max. : 0.235589
## NA's :1 NA's :1c. Using either `arx` or `lm`, run a regression of unemployment on at least one lag of unemployment, inflation and GDP growth (with lags).#using lm (although arx probably better given part d)
lm.reg <- lm(unr ~ unr.1 + gdp.g + gdp.g.1 + infl + infl.1, data=data.f)
summary(lm.reg)##
## Call:
## lm(formula = unr ~ unr.1 + gdp.g + gdp.g.1 + infl + infl.1, data = data.f)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.68635 -0.11649 0.00906 0.11946 0.57683
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.106929 0.032274 3.313 0.00107 **
## unr.1 0.992317 0.004388 226.151 < 2e-16 ***
## gdp.g -4.307051 0.726983 -5.925 1.14e-08 ***
## gdp.g.1 -0.917721 0.760156 -1.207 0.22857
## infl 1.411607 1.206499 1.170 0.24322
## infl.1 5.232749 1.143129 4.578 7.72e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.184 on 229 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9956
## F-statistic: 1.053e+04 on 5 and 229 DF, p-value: < 2.2e-16step(lm.reg)## Start: AIC=-789.74
## unr ~ unr.1 + gdp.g + gdp.g.1 + infl + infl.1
##
## Df Sum of Sq RSS AIC
## - infl 1 0.05 7.80 -790.34
## - gdp.g.1 1 0.05 7.80 -790.25
## <none> 7.75 -789.74
## - infl.1 1 0.71 8.46 -771.17
## - gdp.g 1 1.19 8.94 -758.23
## - unr.1 1 1731.24 1738.99 480.35
##
## Step: AIC=-790.34
## unr ~ unr.1 + gdp.g + gdp.g.1 + infl.1
##
## Df Sum of Sq RSS AIC
## - gdp.g.1 1 0.05 7.84 -790.96
## <none> 7.80 -790.34
## - gdp.g 1 1.14 8.94 -760.23
## - infl.1 1 6.86 14.66 -644.08
## - unr.1 1 1765.78 1773.58 482.97
##
## Step: AIC=-790.96
## unr ~ unr.1 + gdp.g + infl.1
##
## Df Sum of Sq RSS AIC
## <none> 7.84 -790.96
## - gdp.g 1 4.26 12.10 -691.05
## - infl.1 1 7.43 15.27 -636.35
## - unr.1 1 1766.75 1774.60 481.11##
## Call:
## lm(formula = unr ~ unr.1 + gdp.g + infl.1, data = data.f)
##
## Coefficients:
## (Intercept) unr.1 gdp.g infl.1
## 0.09693 0.99167 -4.81527 6.26879library(gets)
arx.reg <- arx(data.f$unr,ar=1:5,mc=T,mxreg=zooreg(data.f[-c(1,grep("unr",colnames(data.f)))]))
arx.reg##
## Date: Tue Mar 3 15:56:26 2015
## Method: Ordinary Least Squares (OLS)
## Variance-Covariance: Ordinary
## No. of observations (mean eq.): 231
## Sample: 6 to 236
##
## Mean equation:
##
## coef std.error t-stat p-value
## mconst 0.03207239 0.02298112 1.3955975 1.642364e-01
## ar1 1.75799515 0.06757266 26.0163658 3.282717e-69
## ar2 -0.75049474 0.13410507 -5.5963189 6.448207e-08
## ar3 -0.07472538 0.14246402 -0.5245210 6.004419e-01
## ar4 0.02827777 0.13226730 0.2137926 8.309059e-01
## ar5 0.03350361 0.06203351 0.5400889 5.896796e-01
## gdp.g -2.34346378 0.52278800 -4.4826273 1.183842e-05
## gdp.g.1 0.92148283 0.54815307 1.6810684 9.416230e-02
## infl 2.20169989 0.84402616 2.6085683 9.712584e-03
## infl.1 -0.16826634 0.86921860 -0.1935835 8.466799e-01
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(6) 3.4144913 6 7.553093e-01
## Ljung-Box ARCH(1) 33.9914011 1 5.535617e-09
## Jarque-Bera 163.1973520 2 0.000000e+00
## R-squared 0.9979854 NA NAd. Run model selection on this, and outlier/break detection methods.isat.reg <- isat(data.f$unr,ar=1:5,mc=T,mxreg=zooreg(data.f[-c(1,grep("unr",colnames(data.f)))]),sis=T)##
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## SIS block 8 of 8...
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##
## GETS of union of retained SIS indicators...
##
##
## GETS of union of ALL retained indicators...
##
## regressor-matrix is column rank deficient, so dropping 2 regressors
##
## Searching path no. 1 out of 1
isat.reg##
## Date: Tue Mar 3 15:56:35 2015
## Method: Ordinary Least Squares (OLS)
## Variance-Covariance: Ordinary
## No. of observations (mean eq.): 231
## Sample (mean eq.): 6 to 236
##
## GUM mean equation:
##
## reg.no keep coef std.error t-stat p-value
## mconst 1 1 0.04680773 0.03151855 1.4850851 1.389997e-01
## ar1 2 1 1.72291164 0.06145632 28.0347332 2.041552e-73
## ar2 3 1 -0.77807254 0.11402720 -6.8235697 9.066915e-11
## ar3 4 1 -0.01008055 0.11508134 -0.0875950 9.302809e-01
## ar4 5 1 0.06898956 0.10689380 0.6454028 5.193608e-01
## ar5 6 1 -0.01888275 0.05091644 -0.3708575 7.111122e-01
## gdp.g 7 1 -2.16653144 0.43890423 -4.9362283 1.605776e-06
## gdp.g.1 8 1 0.77028368 0.46129283 1.6698367 9.642060e-02
## infl 9 1 1.62616814 0.69250193 2.3482507 1.977811e-02
## infl.1 10 1 0.84141267 0.72688642 1.1575573 2.483411e-01
## iis61 11 0 -0.48505428 0.10524655 -4.6087429 6.975714e-06
## iis62 12 0 0.68688562 0.10997376 6.2459045 2.254956e-09
## sis61 13 0 -0.11237633 0.04036519 -2.7839907 5.852637e-03
## sis90 14 0 0.16238079 0.03708494 4.3786180 1.872054e-05
## sis139 15 0 0.19520422 0.05712475 3.4171566 7.579053e-04
## sis143 16 0 -0.20591040 0.05912908 -3.4823879 6.029509e-04
## sis164 17 0 -0.32407056 0.07749526 -4.1818111 4.224977e-05
## sis166 18 0 0.29198408 0.07664250 3.8096890 1.820456e-04
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(6) 5.510171e+00 6 0.48022828
## Ljung-Box ARCH(1) 1.292075e-05 1 0.99713197
## Jarque-Bera 6.576589e+00 2 0.03731745
##
## Paths searched:
##
## path 1 : 13 15 16 18
##
## Terminal models:
##
## spec 1 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## spec 2 : 11 12 14 17 1 2 3 4 5 6 7 8 9 10
##
## info(sc) logl n k
## spec 1 (gum): 3.237491 -324.9485 231 18
## spec 2: -1.355095 194.6104 231 14
##
## SPECIFIC mean equation:
##
## coef std.error t-stat p-value
## mconst 0.09212236 0.02903453 3.1728546 1.728205e-03
## ar1 1.78066822 0.06376966 27.9234382 8.845949e-74
## ar2 -0.86172407 0.11936618 -7.2191642 8.693162e-12
## ar3 -0.01880892 0.12173925 -0.1545017 8.773578e-01
## ar4 0.09572712 0.11282481 0.8484580 3.971179e-01
## ar5 -0.02458151 0.05355460 -0.4589990 6.466943e-01
## gdp.g -2.27176046 0.45541408 -4.9883404 1.246815e-06
## gdp.g.1 0.68913367 0.47868962 1.4396253 1.514145e-01
## infl 1.58022525 0.72675398 2.1743606 3.075956e-02
## infl.1 0.33304251 0.75795676 0.4393951 6.608125e-01
## iis61 -0.54309683 0.10896314 -4.9842254 1.270850e-06
## iis62 0.66515364 0.11426592 5.8211028 2.083935e-08
## sis90 0.16815372 0.03596532 4.6754404 5.152003e-06
## sis164 -0.14067021 0.03259903 -4.3151649 2.423264e-05
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(1) 0.6062682 1 0.4361964
## Ljung-Box ARCH(1) 0.6607086 1 0.4163099
## Jarque-Bera 1.7593833 2 0.4149108#now want found dummies to insert into original regression (so diagnostic tests pass)
isat.dums <- isat.reg$aux$mX[,grep("is\\d+$",isat.reg$aux$mXnames)]
#lack first five observations so add zeros
isat.dums <- rbind(matrix(0,5,4),isat.dums)
#add to existing dataset
data.f <- cbind(data.f,isat.dums)
arx.reg.2 <- arx(data.f$unr,ar=1:5,mc=T,mxreg=zooreg(data.f[-c(1,grep("unr",colnames(data.f)))]))
arx.reg.2##
## Date: Tue Mar 3 15:56:35 2015
## Method: Ordinary Least Squares (OLS)
## Variance-Covariance: Ordinary
## No. of observations (mean eq.): 231
## Sample: 6 to 236
##
## Mean equation:
##
## coef std.error t-stat p-value
## mconst 0.09212236 0.02903453 3.1728546 1.728205e-03
## ar1 1.78066822 0.06376966 27.9234382 8.845949e-74
## ar2 -0.86172407 0.11936618 -7.2191642 8.693162e-12
## ar3 -0.01880892 0.12173925 -0.1545017 8.773578e-01
## ar4 0.09572712 0.11282481 0.8484580 3.971179e-01
## ar5 -0.02458151 0.05355460 -0.4589990 6.466943e-01
## gdp.g -2.27176046 0.45541408 -4.9883404 1.246815e-06
## gdp.g.1 0.68913367 0.47868962 1.4396253 1.514145e-01
## infl 1.58022525 0.72675398 2.1743606 3.075956e-02
## infl.1 0.33304251 0.75795676 0.4393951 6.608125e-01
## iis61 -0.54309683 0.10896314 -4.9842254 1.270850e-06
## iis62 0.66515364 0.11426592 5.8211028 2.083935e-08
## sis90 0.16815372 0.03596532 4.6754404 5.152003e-06
## sis164 -0.14067021 0.03259903 -4.3151649 2.423264e-05
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(6) 7.1643797 6 0.3059128
## Ljung-Box ARCH(1) 0.6607086 1 0.4163099
## Jarque-Bera 1.7593833 2 0.4149108
## R-squared 0.9985679 NA NAgets.m <- getsm(arx.reg.2)## Searching path no. 1 out of 5
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gets.m##
## Date: Tue Mar 3 15:56:35 2015
## Method: Ordinary Least Squares (OLS)
## Variance-Covariance: Ordinary
## No. of observations (mean eq.): 231
## Sample (mean eq.): 6 to 236
##
## GUM mean equation:
##
## reg.no keep coef std.error t-stat p-value
## mconst 1 0 0.09212236 0.02903453 3.1728546 1.728205e-03
## ar1 2 0 1.78066822 0.06376966 27.9234382 8.845949e-74
## ar2 3 0 -0.86172407 0.11936618 -7.2191642 8.693162e-12
## ar3 4 0 -0.01880892 0.12173925 -0.1545017 8.773578e-01
## ar4 5 0 0.09572712 0.11282481 0.8484580 3.971179e-01
## ar5 6 0 -0.02458151 0.05355460 -0.4589990 6.466943e-01
## gdp.g 7 0 -2.27176046 0.45541408 -4.9883404 1.246815e-06
## gdp.g.1 8 0 0.68913367 0.47868962 1.4396253 1.514145e-01
## infl 9 0 1.58022525 0.72675398 2.1743606 3.075956e-02
## infl.1 10 0 0.33304251 0.75795676 0.4393951 6.608125e-01
## iis61 11 0 -0.54309683 0.10896314 -4.9842254 1.270850e-06
## iis62 12 0 0.66515364 0.11426592 5.8211028 2.083935e-08
## sis90 13 0 0.16815372 0.03596532 4.6754404 5.152003e-06
## sis164 14 0 -0.14067021 0.03259903 -4.3151649 2.423264e-05
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(6) 7.1643797 6 0.3059128
## Ljung-Box ARCH(1) 0.6607086 1 0.4163099
## Jarque-Bera 1.7593833 2 0.4149108
##
## Paths searched:
##
## path 1 : 4 6 10 8
## path 2 : 5 10 4 8 6 -6
## path 3 : 6 4 10 8
## path 4 : 8 4 6 10
## path 5 : 10 4 6 8
##
## Terminal models:
##
## spec 1 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14
## spec 2 : 1 2 3 5 7 9 11 12 13 14
## spec 3 : 1 2 3 7 9 11 12 13 14 6
##
## info(sc) logl n k
## spec 1 (gum): 3.143823 -325.0146 231 14
## spec 2: -1.437120 193.1994 231 10
## spec 3: -1.432945 192.7172 231 10
##
## SPECIFIC mean equation:
##
## coef std.error t-stat p-value
## mconst 0.09964363 0.02713925 3.671570 3.023382e-04
## ar1 1.78047769 0.05681561 31.337826 2.861002e-83
## ar2 -0.86370347 0.07636828 -11.309715 1.070079e-23
## ar4 0.05491079 0.02559062 2.145739 3.298397e-02
## gdp.g -1.78886277 0.34177246 -5.234075 3.849793e-07
## infl 2.06966030 0.33333729 6.208907 2.610012e-09
## iis61 -0.53291663 0.10796571 -4.935980 1.569956e-06
## iis62 0.66787823 0.11324919 5.897422 1.371156e-08
## sis90 0.16805386 0.03447422 4.874769 2.079686e-06
## sis164 -0.14432157 0.03106127 -4.646351 5.803478e-06
##
## Diagnostics:
##
## Chi-sq df p-value
## Ljung-Box AR(6) 7.4499114 6 0.2812340
## Ljung-Box ARCH(1) 0.5488519 1 0.4587872
## Jarque-Bera 1.1509321 2 0.5624427e. Select a training period and evaluate the forecasts your model creates.data.f.0 <- data.f[1:230,]
data.f.1 <- data.f[231:236,]
library(forecast)## Loading required package: timeDate
## This is forecast 5.8forc.mod.0 <- Arima(data.f.0$unr,order=c(4,0,0),xreg=zooreg(data.f.0[-c(1,grep("unr",colnames(data.f.0)))]))
forc.0 <- forecast(forc.mod.0,h=6,xreg=zooreg(data.f.1[-c(1,grep("unr",colnames(data.f.1)))]))
plot(forc.0,include=100)
accuracy(forc.0,data.f.1$unr)## ME RMSE MAE MPE MAPE
## Training set 0.003834849 0.1175692 0.08979836 0.02280558 2.817975
## Test set -0.688445035 0.7774792 0.68844503 -22.34160016 22.341600
## MASE ACF1
## Training set 0.497111 -0.004044291
## Test set 3.811134 NA- Manual download:
- Download data on David Cameron, Nick Clegg, Nigel Farage and Ed Miliband from Google Trends, and manipulate the data so it can be imported into R.
ldr <- read.csv("/home/readejj/Dropbox/Teaching/Reading/ec313/2015/midterm-code/leaders.csv",stringsAsFactors=F)
ldr$date <- as.Date(substr(ldr$Week,1,10))
#for purposes of simplicity, aggregating to monthly data preferable
ldr$ym <- format(ldr$date,"%Y-%m")
ldr.m <- aggregate(ldr[,2:5],by=list(ldr$ym),FUN=mean)b. Find the "best" ARIMA model for David Cameron. How well does it forecast?dave.t <- ts(ldr.m$David.Cameron,start=c(2004,1),freq=12)
dave.t.0 <- window(dave.t,end=c(2014,6))
dave.t.1 <- window(dave.t,start=c(2014,7))
dave.t.auto <- auto.arima(dave.t) #more marks for follownig manual process to get best ARIMA order!
dave.arima.0 <- Arima(dave.t.0,order=c(1,1,1))
dave.arima.f <- forecast(dave.arima.0,h=8)
plot(window(dave.t,start=c(2013,1)))
lines(dave.arima.f$mean,col=2)
c. Find the "best" exponential smoothing model for David Cameron. How well does it forecast?dave.t.ets <- ets(dave.t)
dave.ets.0 <- ets(dave.t.0,model="ANN")
dave.ets.f <- forecast(dave.ets.0,h=8)
plot(window(dave.t,start=c(2013,1)))
lines(dave.arima.f$mean,col=2)
lines(dave.ets.f$mean,col=3)
legend("topleft",lty=1,col=c(1,2,3),legend=c("Actual","ARIMA","ETS"))
d. Find the "best" time series decomposition model for David Cameron. How well does it forecast?dave.t.ts <- stl(dave.t,s.window=8,t.window=5)
dave.ts.0 <- stl(dave.t.0,s.window=8,t.window=5)
dave.ts.f <- forecast(dave.ts.0,h=8)
plot(window(dave.t,start=c(2013,1)),
ylim=range(c(window(dave.t,start=c(2013,1)),dave.arima.f$mean,dave.ets.f$mean,dave.ts.f$mean)))
lines(dave.arima.f$mean,col=2)
lines(dave.ets.f$mean,col=3)
lines(dave.ts.f$mean,col=4)
legend("topleft",lty=1,col=c(1,2,3,4),legend=c("Actual","ARIMA","ETS","TS"))
e. Which model is best, and do any of the other leaders help in forecasting?ldr.t <- ts(ldr.m[,2:5],start=c(2004,1),freq=12)
ldr.t.0 <- window(ldr.t,end=c(2014,6))
ldr.t.1 <- window(ldr.t,start=c(2014,7))
dave.t.mod <- Arima(ldr.t.0[,1],order=c(1,1,1),xreg=ldr.t.0[,2:4])
dave.t.f <- forecast(dave.t.mod,xreg=ldr.t.1[,2:4])
plot(window(dave.t,start=c(2013,1)),
ylim=range(c(window(dave.t,start=c(2013,1)),dave.arima.f$mean,
dave.ets.f$mean,dave.ts.f$mean,dave.t.f$mean)))
lines(dave.arima.f$mean,col=2)
lines(dave.ets.f$mean,col=3)
lines(dave.ts.f$mean,col=4)
lines(dave.t.f$mean,col=5)
legend("topleft",lty=1,col=c(1,2,3,4,5),legend=c("Actual","ARIMA","ETS","TS","Other"),bty="n")
Answer appears to be “yes”, other leaders help, but bear in mind that this model cheats in the sense that these forecasts are made knowing the popularity of other leaders in a given month. A better test would be to look at lagged popularity of leaders. What this model appears to suggest is that there are likely reasons why politicians get less coverage in particular weeks, for example if some big sporting event takes place distracting news attention away from politicians.