Exercise 3.1

For the following series, find an appropriate Box-Cox transformation in order to stabilise the variance.

## [1] 0.5167714

## [1] 0.366352

## [1] 0.1919047

## [1] -0.2269461

Exercise 3.2

Why is a Box-Cox transformation unhelpful for the cangas data?

## [1] 0.5767759

##         Jan    Feb    Mar    Apr    May    Jun
## 1960 1.4306 1.3059 1.4022 1.1699 1.1161 1.0113
##             Jan        Feb        Mar        Apr        May        Jun
## 1960 0.39775735 0.28853071 0.37324769 0.16423852 0.11339450 0.01127312
Box-Cox transformation on the Cangas dataset has minimal impact on the stabilization of the variance. The scale and shape of the plotted time series is very similar to the original. The seasonal variation was not affected after the transformation

Exercise 3.3

What Box-Cox transformation would you select for your retail data (from Exercise 3 in Section 2.10)?

## [1] 0.1276369
## Warning in `/.default`(0.5 * fvar * (1 - lambda), (out)^(2 * lambda)): Recycling array of length 1 in array-vector arithmetic is deprecated.
##   Use c() or as.vector() instead.

A Bias-adjusted Box-Cox transformation seems to be a better choice with a lambda value of 0.1276

Exercise 3.8

For your retail time series (from Exercise 3 in Section 2.10):

Split the data into two parts using

Check that your data have been split appropriately by producing the following plot.

Calculate forecasts using snaive applied to myts.train.

Compare the accuracy of your forecasts against the actual values stored in myts.test.

##                     ME     RMSE      MAE       MPE      MAPE     MASE
## Training set  7.772973 20.24576 15.95676  4.702754  8.109777 1.000000
## Test set     55.300000 71.44309 55.78333 14.900996 15.082019 3.495907
##                   ACF1 Theil's U
## Training set 0.7385090        NA
## Test set     0.5315239  1.297866

Check the residuals.

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 624.45, df = 24, p-value < 2.2e-16
## 
## Model df: 0.   Total lags used: 24

Do the residuals appear to be uncorrelated and normally distributed?

Residuals appear to be correlated as per ACF chart and with mean \(\neq\) 0; also, they almost look normally distributed even though the left tail seems not very symmetric to the right tail. Variation of residuals seems not constant.

How sensitive are the accuracy measures to the training/test split?

Accuracy measures seem to be more sensitive to the test split, the magnitude is considerable higher than the training split across all of them.