Discussion 6

Load Data

setwd("~/Documents/MSAE/Predictive Analytics")
retaildata <- read.csv("retaildata.csv")

Creating Tsibble

retaildata  <- retaildata  %>% 
  mutate(Month = yearmonth(Month)) %>% 
  tsibble(index = Month)

retaildata$Retail = as.numeric(retaildata$Retail)

Training Set (1993-2018) & Test Set (2019)

training <- retaildata %>% 
  filter(year(Month) < 2019 )

test <- retaildata %>% 
  filter(year(Month) == 2019)

Time-Series Plot

training %>% autoplot() + 
  labs(title = "Monthly Sales for Total Retail Sales, 1993-2018") +
  xlab("Month") +
  ylab("Sales ($ in Millions)") 

## Plot variable not specified, automatically selected `.vars = Retail`

Seasonal Plot

training %>% gg_season(Retail) + 
  labs(title = "Seasonality of Retail Sales") +
  xlab("Month") +
  ylab("Sales ($ in Millions)") 

Neural Net Model

neuralnet_model <- training %>% model(NNETAR(log(Retail)))
report(neuralnet_model)

## Series: Retail 
## Model: NNAR(1,1,2)[12] 
## Transformation: log(Retail) 
## 
## Average of 20 networks, each of which is
## a 2-2-1 network with 9 weights
## options were - linear output units 
## 
## sigma^2 estimated as 0.001233

neuralnet_fcst <- neuralnet_model %>% forecast(test)


 neuralnet_fcst %>% autoplot(training) + 
  labs(title = "Neural Net model") +
  xlab("Month") +
  ylab("Sales ($ in Millions)") 

neuralnet_fcst %>% autoplot(test) + 
  labs(title = "Neural Net model") +
  xlab("Month") +
  ylab("Sales ($ in Millions)") 

nn_accuracy <- accuracy(neuralnet_fcst, test)

ARIMA

ARIMA_model <- training %>% 
  model(ARIMA(log(Retail)))

ARIMA_fcst <- ARIMA_model %>% forecast(test)
ARIMA_plot <- ARIMA_model %>% forecast(test) %>% autoplot(test) + 
  labs(title = "ARIMA model") +
  xlab("Month") +
  ylab("Sales ($ in Millions)") 
ARIMA_accuracy <- accuracy(ARIMA_fcst, test)

report(ARIMA_model)

## Series: Retail 
## Model: ARIMA(2,1,1)(0,1,1)[12] 
## Transformation: log(Retail) 
## 
## Coefficients:
##           ar1      ar2     ma1     sma1
##       -0.9444  -0.5358  0.3599  -0.7502
## s.e.   0.0887   0.0554  0.0955   0.0450
## 
## sigma^2 estimated as 0.0004077:  log likelihood=741.59
## AIC=-1473.18   AICc=-1472.98   BIC=-1454.68

ARIMA_model %>% gg_tsresiduals(lag_max = 12) + labs(title = "ARIMA model")

ARIMA_plot

ETS model

ETS_model <- training %>% 
  model(ETS(log(Retail)))


ETS_fcst <- ETS_model %>% forecast(test)
ETS_plot <- ETS_model %>% forecast(test) %>% autoplot(test) + 
  labs(title = "ETS model")+
  xlab("Month") +
  ylab("Sales ($ in Millions)") 
ETS_accuracy <- accuracy(ETS_fcst, test)


report(ETS_model)

## Series: Retail 
## Model: ETS(A,Ad,A) 
## Transformation: log(Retail) 
##   Smoothing parameters:
##     alpha = 0.4632852 
##     beta  = 0.02082179 
##     gamma = 0.1708057 
##     phi   = 0.9799992 
## 
##   Initial states:
##      l[0]        b[0]      s[0]      s[-1]        s[-2]       s[-3]      s[-4]
##  11.92483 0.008770624 0.1910545 0.01162845 -0.008418121 -0.03626672 0.02312176
##        s[-5]      s[-6]      s[-7]        s[-8]       s[-9]     s[-10]
##  0.006584932 0.01812502 0.03780529 -0.007010001 0.003748631 -0.1284263
##      s[-11]
##  -0.1119474
## 
##   sigma^2:  4e-04
## 
##       AIC      AICc       BIC 
## -595.5131 -593.1786 -528.1390

ETS_model %>% gg_tsresiduals(lag_max = 12) + labs(title="ETS Model")

ETS_plot 

Accuracy Metrics and Discussion

accuracy_metrics = rbind("ETS" = ETS_accuracy, 
                         "ARIMA" = ARIMA_accuracy,
                         "Neural Network" = nn_accuracy
                         )
accuracy_metrics <- accuracy_metrics %>% arrange(RMSE)
accuracy_metrics

## # A tibble: 3 × 10
##   .model              .type     ME  RMSE   MAE    MPE  MAPE  MASE RMSSE    ACF1
## * <chr>               <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>   <dbl>
## 1 ARIMA(log(Retail))  Test   2063. 6731. 5700.  0.396  1.28   NaN   NaN -0.0736
## 2 NNETAR(log(Retail)) Test  -3803. 7986. 6221. -0.934  1.43   NaN   NaN -0.155 
## 3 ETS(log(Retail))    Test   5701. 9624. 8137.  1.19   1.79   NaN   NaN  0.226