Data 624 Project
Charls Joseph
10/25/2020
Data 624 Project
Part A – ATM Forecast, ATM624Data.xlsx
In part A, I want you to forecast how much cash is taken out of 4 different ATM machines for May 2010. The data is given in a single file. The variable ‘Cash’ is provided in hundreds of dollars, other than that it is straight forward. I am being somewhat ambiguous on purpose to make this have a little more business feeling. Explain and demonstrate your process, techniques used and not used, and your actual forecast. I am giving you data via an excel file, please provide your written report on your findings, visuals, discussion and your R code via an RPubs link along with the actual.rmd file Also please submit the forecast which you will put in an Excel readable file.
atmdata <- readxl::read_excel('C:\\Users\\charls.joseph\\Documents\\Cuny\\Data624\\project1\\ATM624Data.xlsx')
atmdf <- atmdata %>%
drop_na() %>%
spread(ATM, Cash) %>%
mutate(DATE = as.Date(DATE, origin='1899-12-30'))
head(atmdf)## # A tibble: 6 x 5
## DATE ATM1 ATM2 ATM3 ATM4
## <date> <dbl> <dbl> <dbl> <dbl>
## 1 2009-05-01 96 107 0 777.
## 2 2009-05-02 82 89 0 524.
## 3 2009-05-03 85 90 0 793.
## 4 2009-05-04 90 55 0 908.
## 5 2009-05-05 99 79 0 52.8
## 6 2009-05-06 88 19 0 52.2Lets check the pattern for 4 ATM data.
atmdf %>% gather(atm, Cash, -DATE) %>%
ggplot(aes(x = DATE, y = Cash, col = atm)) +
geom_line(show.legend = FALSE) +
facet_wrap(~ atm, ncol = 1, scales = "free_y") +
labs(title = "Withdrawals from different ATMs", subtitle = "from May-2009 - Apr-2010", x = "Date") +
scale_y_continuous("withdrawals - Amount")
Below are the observation
ATM1 - There is a weekly seasonality, but no trend. ATM2 - There is a weekly seasonality, but no trend. ATM3 - There are some non zero values for the last 1-2 weeks. ATM4 - Do not see a seasonality or trend, but seeing an outlier.
atm1_ts <- ts(atmdf[, "ATM1"], frequency = 7)
atm2_ts <- ts(atmdf[, "ATM2"] , frequency = 7)
atm3_ts <- ts(atmdf[, "ATM3"], frequency = 7)
atm4_ts <- ts(atmdf[, "ATM4"], frequency = 7)ggtsdisplay(atm1_ts, points = FALSE, main = "Withdrawals ATM1", xlab = "Day", ylab = "Cash Amounts")
Lets make this stationary and analyze AR and MA component. In order to make it stationary, we need to make the variance and apply a seasonal lag difference .
atm1_lambda <- BoxCox.lambda(atm1_ts)
atm1_bc <- atm1_ts %>% BoxCox(atm1_lambda)
atm1_bc_diff <- atm1_bc %>% diff(lag=7)
ggtsdisplay(atm1_bc_diff, points = FALSE, main = "with transformation and differencing", xlab = "Day", ylab = "Cash Amounts")
Observation from ATM1 plots
From ACF plot, there is a significant correlation on every 7 lags which indicate this is seasonal. From PACF plot, there is a significant correlation on lag 7, 14 and 21. However it is gradually settled down.
This indicate that we may need to use seasonal ARIMA to model this pattern.
After applying transformation and difference From ACF plots, we can see that there is high correlation on lag 1 which indicate non seasonal MA(1) high correlation on lag 7 may indicate a seasonal MA(1) component.
From PACF plots, we can see that there is high correlation on lag 1 which indicate non seasonal AR(1) high correlation on lag 7,14,21 may indicate a seasonal AR(3) component.
Later, we will rely in getting the order from Auto.Arima() function since it has non seasonal and seasonal.
Lets look at the patter for ATM 2
ggtsdisplay(atm2_ts, points = FALSE, main = "Withdrawals ATM2", xlab = "Day", ylab = "Cash Amounts")
Lets make this stationary and analyze AR and MA component. In order to make it stationary, we need to make the variance and apply a seasonal lag difference.
atm2_lambda <- BoxCox.lambda(atm2_ts)
atm2_bc <- atm2_ts %>% BoxCox(atm2_lambda)
atm2_bc_diff <- atm2_bc %>% diff(lag=7)
ggtsdisplay(atm2_bc_diff, points = FALSE, main = "with transformation and differencing", xlab = "Day", ylab = "Cash Amounts")
Observation from ATM2 plots
From ACF plot, there is a significant correlation on every 7 lags which indicate this is seasonal. From PACF plot, there is a significant correlation on lag 7, 14 and 21. However it is gradually settled down.
After applying transformation and difference From ACF plots, we can see that there is high correlation on lag 7 may indicate a seasonal MA(1) component. But there is no non-seasonal MA component.
From PACF plots, we can see that high correlation on lag 7,14,21 may indicate a seasonal AR(3) component. But there is no non-seasonal AR component.
This is very similar for ATM 1. We will use seasonal ARIMA model to model this pattern
Lets look at the ATM-3 plots
ggtsdisplay(atm3_ts, points = FALSE, main = "Withdrawals ATM3", xlab = "Day", ylab = "Cash Amounts")
#### Observation from ATM3 plots
From ACF plots, there are significant auto-correlation for the lag 1,2. From PACF, the auto correlation gradually slow down.
Lets look at the ATM-3 plots
ggtsdisplay(atm4_ts, points = FALSE, main = "Withdrawals ATM3", xlab = "Day", ylab = "Cash Amounts")
Observation from ATM4 plots
From ACF plots and PACF, there is no significant auto correlation.
Modeling
atm1_lambda <- BoxCox.lambda(atm1_ts)
atm2_lambda <- BoxCox.lambda(atm2_ts)
arima_atm1 <- auto.arima(atm1_ts)
arima_atm2 <- auto.arima(atm2_ts)summary(arima_atm1)## Series: atm1_ts
## ARIMA(1,0,0)(2,1,0)[7]
##
## Coefficients:
## ar1 sar1 sar2
## 0.1511 -0.4698 -0.2048
## s.e. 0.0535 0.0517 0.0514
##
## sigma^2 estimated as 606.7: log likelihood=-1641.05
## AIC=3290.11 AICc=3290.22 BIC=3305.63
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.08937144 24.28804 15.37384 -98.72979 115.434 0.8697514
## ACF1
## Training set 0.009201474summary(arima_atm2)## Series: atm2_ts
## ARIMA(0,0,0)(2,1,0)[7]
##
## Coefficients:
## sar1 sar2
## -0.5747 -0.1766
## s.e. 0.0521 0.0518
##
## sigma^2 estimated as 652.8: log likelihood=-1659.31
## AIC=3324.61 AICc=3324.68 BIC=3336.26
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1179362 25.23195 17.27829 -Inf Inf 0.8434248 0.01502367Auto Arima function suggested ARIMA(1,0,0)(2,1,0)[7] for ATM1 and ATM2 time series data. Please note there is a differencing needed with 7 lags as indicated in ACF and PACF.
Lets check the residual for ATM1
checkresiduals(arima_atm1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,0)(2,1,0)[7]
## Q* = 18.297, df = 11, p-value = 0.07494
##
## Model df: 3. Total lags used: 14The residuals are normally distributed
Lets check the residual for ATM2
checkresiduals(arima_atm2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,0,0)(2,1,0)[7]
## Q* = 28.213, df = 12, p-value = 0.005149
##
## Model df: 2. Total lags used: 14The residuals are normally distributed
Lets do modeling for ATM3. Since there is no trend or seasonality, we will try the mean and naive model.
atm3_mean <- meanf(atm3_ts, h = 14)
atm3_naive <- naive(atm3_ts, h = 14)
autoplot(atm3_ts) +
autolayer(atm3_mean, series = "Average", PI = FALSE) +
autolayer(atm3_naive, series = "Naive", PI = FALSE) 
checkresiduals(atm3_mean)
##
## Ljung-Box test
##
## data: Residuals from Mean
## Q* = 196.67, df = 13, p-value < 2.2e-16
##
## Model df: 1. Total lags used: 14Finally lets do the modeling for ATM 4. We will try auto.arima().
atm4_lambda <- BoxCox.lambda(atm4_ts)
arima_atm4 <- auto.arima(atm4_ts)
summary(arima_atm4)## Series: atm4_ts
## ARIMA(0,0,0) with non-zero mean
##
## Coefficients:
## mean
## 474.0433
## s.e. 34.0248
##
## sigma^2 estimated as 423718: log likelihood=-2882.03
## AIC=5768.06 AICc=5768.1 BIC=5775.86
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -1.514697e-10 650.0437 323.6001 -616.5219 646.8627 0.8051872
## ACF1
## Training set -0.009358419checkresiduals(arima_atm4)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,0,0) with non-zero mean
## Q* = 4.6668, df = 13, p-value = 0.9818
##
## Model df: 1. Total lags used: 14Fitting the model.
ATM1 forecast
atm1_fit<-Arima(atm1_ts, order = c(1, 0, 0), seasonal = c(2, 1, 0), lambda = atm1_lambda)
atm1_forecast<-forecast(atm1_fit, 31) ## forecast for the 31 days.
autoplot(atm1_ts) +
autolayer(atm1_forecast, series = "Arima forcasted - ATM 1", PI = FALSE) 
#### ATM2 forecast
atm2_fit<-Arima(atm2_ts, order = c(1, 0, 0), seasonal = c(2, 1, 0), lambda = atm2_lambda)
atm2_forecast<-forecast(atm2_fit, 31) ## forecast for the 31 days.
autoplot(atm2_ts) +
autolayer(atm2_forecast, series = "Arima forcasted ATM 2 ", PI = FALSE) 
#### ATM3 forecast
atm3_naive <- naive(atm3_ts, h = 31)
autoplot(atm3_ts) +
autolayer(atm3_naive, series = "Naive forecasting - ATM 3 ", PI = FALSE) 
#### ATM4 forecast
atm4_fit<-Arima(atm4_ts, order = c(0, 0, 0), lambda = atm4_lambda)
atm4_forecast<-forecast(atm4_fit, 31) ## forecast for the 31 days.
autoplot(atm4_ts) +
autolayer(atm2_forecast, series = "Arima forcasted ATM 2 ", PI = FALSE) 
max(atmdf$DATE) ## [1] "2010-04-30"names(atmdf)[-1]## [1] "ATM1" "ATM2" "ATM3" "ATM4"results <- data_frame(DATE = rep(max(atmdf$DATE) + 1:31, 4), ATM = rep(names(atmdf)[-1], each = 31), Cash = c(atm1_forecast$mean, atm2_forecast$mean,atm3_naive$mean, atm4_forecast$mean)) ## Warning: `data_frame()` is deprecated as of tibble 1.1.0.
## Please use `tibble()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.## write_csv(results, "DATA624_partA_Forecast_Results.csv")Part B – Forecasting Power, ResidentialCustomerForecastLoad-624.xlsx
Part B consists of a simple dataset of residential power usage for January 1998 until December 2013. Your assignment is to model these data and a monthly forecast for 2014. The data is given in a single file. The variable ‘KWH’ is power consumption in Kilowatt hours, the rest is straight forward. Add this to your existing files above.
powerdf <- readxl::read_excel('C:\\Users\\charls.joseph\\Documents\\Cuny\\Data624\\project1\\ResidentialCustomerForecastLoad-624.xlsx')
head(powerdf)## # A tibble: 6 x 3
## CaseSequence `YYYY-MMM` KWH
## <dbl> <chr> <dbl>
## 1 733 1998-Jan 6862583
## 2 734 1998-Feb 5838198
## 3 735 1998-Mar 5420658
## 4 736 1998-Apr 5010364
## 5 737 1998-May 4665377
## 6 738 1998-Jun 6467147powerts <- ts(powerdf[, "KWH"], start = c(1998, 1), frequency = 12)ggtsdisplay(powerts, points = FALSE, main = "Monthly Power Usage 01/98 - 12/13 ", xlab = "Years", ylab = "Power Usage")
From the above plot, we see that there is seasonality, but no trend.
Modeling
We will try use Auto.Arima to determine the order of the ARIMA since there is a seasonal component.
power_lambda <- BoxCox.lambda(powerts)
power_trans <- BoxCox(powerts, power_lambda)
fc_arima_power <- auto.arima(powerts)
summary(fc_arima_power)## Series: powerts
## ARIMA(0,0,2)(2,1,0)[12] with drift
##
## Coefficients:
## ma1 ma2 sar1 sar2 drift
## 0.1739 0.0505 -0.7591 -0.4124 8750.907
## s.e. 0.0766 0.0844 0.0697 0.0682 3214.839
##
## sigma^2 estimated as 7.841e+11: log likelihood=-2707.12
## AIC=5426.25 AICc=5426.73 BIC=5445.4
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -9730.731 845160.6 506279.9 -5.055329 11.57781 0.730904
## ACF1
## Training set 0.008533477Fitting
power_fit<-Arima(powerts, order = c(0, 0,2), seasonal = c(2,1,0), lambda = power_lambda)
power_forecast<-forecast(power_fit, 12) ## forecast for the 31 days.
ggtsdisplay(resid(power_fit), points = FALSE, plot.type = "histogram", main = "Residuals for ARIMA(2,1,1)(0,0,2) of power consumption", xlab = "Year", ylab = "Residual")## Warning: Removed 1 rows containing non-finite values (stat_bin).
autoplot(power_forecast) +
labs(title = "Energy Forecast for 2014", x = "Month", y = "kWh") +
theme(legend.position = "none")
Results
result <- data_frame(`YYYY-MMM` = paste0(2014, "-", month.abb), KWH = power_forecast$mean)
# write_csv(result, "DATA624_partB_Power_Results.csv")Part C ( Bonus Question)
Requirement
Part C consists of two data sets. These are simple 2 columns sets, however they have different time stamps. Your optional assignment is to time-base sequence the data and aggregate based on hour (example of what this looks like, follows). Note for multiple recordings within an hour, take the mean. Then to determine if the data is stationary and can it be forecast. If so, provide a week forward forecast and present results via Rpubs and .rmd and the forecast in an Excel readable file.
We will first load the two dataset and observe a sample
water1 <- readxl::read_excel('C:\\Users\\charls.joseph\\Documents\\Cuny\\Data624\\project1\\Waterflow_Pipe1.xlsx', col_types = c("date","numeric"))
water2 <- readxl::read_excel('C:\\Users\\charls.joseph\\Documents\\Cuny\\Data624\\project1\\Waterflow_Pipe2.xlsx', col_types = c("date","numeric"))
head(water1)## # A tibble: 6 x 2
## `Date Time` WaterFlow
## <dttm> <dbl>
## 1 2015-10-23 00:24:06 23.4
## 2 2015-10-23 00:40:02 28.0
## 3 2015-10-23 00:53:51 23.1
## 4 2015-10-23 00:55:40 30.0
## 5 2015-10-23 01:19:17 6.00
## 6 2015-10-23 01:23:58 15.9head(water2)## # A tibble: 6 x 2
## `Date Time` WaterFlow
## <dttm> <dbl>
## 1 2015-10-23 01:00:00 18.8
## 2 2015-10-23 02:00:00 43.1
## 3 2015-10-23 03:00:00 38.0
## 4 2015-10-23 04:00:00 36.1
## 5 2015-10-23 05:00:00 31.9
## 6 2015-10-23 06:00:00 28.2#join them
water <- rbind(water1,water2)
water <- water[order(as.Date(water$`Date Time`, format="%Y-m%-d% h%:M%:s%")),]
#aggragate by hour and take mean...
water <- water %>%
separate(`Date Time`, into = c("date", "time"), sep = " ") %>%
separate(time, into = c("hour", "minute", "seccond"), sep = ":") %>%
group_by(date, hour) %>%
summarise(mean(WaterFlow,na.rm = T)) %>%
ungroup() %>%
arrange() %>%
collect() %>%
`colnames<-`(c("date", "time", "WaterFlow"))## `summarise()` regrouping output by 'date' (override with `.groups` argument)water_ts <- ts(water$WaterFlow,frequency=24)
head(water_ts)## Time Series:
## Start = c(1, 1)
## End = c(1, 6)
## Frequency = 24
## [1] 26.10280 18.84515 24.46806 25.56366 22.36159 23.63798ggtsdisplay(water_ts, points = FALSE, main = "Water flow - hourly", xlab = "Date(hourly)", ylab = "Water flow")
This plot indicate that there is high variance. we dont see a trend or seasionality in this data. Lets make this series stationary by applying tranformation and differencing(lag=1)
water_lambda <- BoxCox.lambda(water_ts)
water_bc <- BoxCox(water_ts, water_lambda)
water_bc_d <- water_bc %>% diff()
ggtsdisplay(water_bc_d, points = FALSE, main = "Water flow - After tranformation and difference", xlab = "Date(hourly)", ylab = "Water flow")
From the ACF and PACF plots, we are seeing that there is high correlation on lag 1 and exponential decay for PACF. This indicate an MA(1) non seasonal model with d =1
water_fit <- Arima(water_ts, order = c(0, 1,1), lambda = water_lambda)
water_fc<-forecast(water_fit, 168) ## forecast for the 168 observation( 7* 24 hours).
summary(water_fit)## Series: water_ts
## ARIMA(0,1,1)
## Box Cox transformation: lambda= -0.4973507
##
## Coefficients:
## ma1
## -0.9794
## s.e. 0.0065
##
## sigma^2 estimated as 0.01188: log likelihood=796.49
## AIC=-1588.98 AICc=-1588.97 BIC=-1579.16
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 5.970137 15.94753 12.06652 -7.811153 42.86658 0.7980706 0.02200742autoplot(water_fc) +
labs(title = "Water flow - hourly - MA(1) ", x = "Date - Hourly", y = "water flow") +
theme(legend.position = "none")
tail(water)## # A tibble: 6 x 3
## date time WaterFlow
## <chr> <chr> <dbl>
## 1 2015-12-03 11 73.0
## 2 2015-12-03 12 31.5
## 3 2015-12-03 13 66.8
## 4 2015-12-03 14 42.9
## 5 2015-12-03 15 33.4
## 6 2015-12-03 16 66.7library(lubridate) ##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionwater_result <- data.frame(water_fc$mean)
colnames(water_result) <- "WaterFlow"
row.names(water_result) <- seq(ymd_hm("2015-12-3 17:00"), ymd_hm("2015-12-10 16:00"), by = "hour")
water_result## WaterFlow
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## 2015-12-10 16:00:00 35.02095Lets try Auto.Arima() to determine p,q,d
fc_arima_water <- auto.arima(water_ts, seasonal = F)
summary(fc_arima_water)## Series: water_ts
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.9629
## s.e. 0.0083
##
## sigma^2 estimated as 212.9: log likelihood=-4100.12
## AIC=8204.24 AICc=8204.25 BIC=8214.05
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.531199 14.57593 11.14363 -26.38446 47.91859 0.7370315
## ACF1
## Training set -0.02311872Auto.Arima() suggested ARIMA(0,1,1).