This blog piece intends to introduce a new addin (i.e. BOXCOX) that can be used in applying power transformations to the series of interest and provides alternative methods to estimate the optimal lambda parameter to be used in transformation.
Table of Contents
 Introduction
 BoxCox family of transformations
 Application to Turkey’s tourism data
 Files
 References
Introduction
A stationary time series requires stable mean and variance, which can then be modelled through ARMAtype models. If a series does not have a finite variance, it violates this condition and will lead to illdefined models. Common practice in dealing with time varying volatility is modeling the variance explicitly through GARCHtype models. However, when the variance of a given series changes with respect to the level, then there is a practical alternative: transforming the original series so as to scale down (up) the large (small) values.BoxCox family of transformations
Box and Cox (1964) proposed a family of power transformations, which later became a popular tool in time series analysis to deal with skewness in the data:$$ \tilde{y}_t = \begin{cases} \frac{y_t^\lambda  1}{\lambda} & \text{if } \lambda \neq 0\\ log(y_t) & \text{if } \lambda = 0 \end{cases} $$ Transformation of a series is straightforward once the value of $\lambda$ is known. One way to determine the value of $\lambda$ is to maximize the (regular or profile) log likelihood of a linear regression model fitted to data. For trending and/or seasonal data, appropriate dummy variables are added to regressions to capture such effects. Guerrero (1993) proposed a modelindependent method to select $\lambda$ that minimizes the coefficient of variation for the subsets of series.
Application to Turkey’s Tourism Data
With its pervasive trend and seasonal components, monthly tourism statistics emerge as a natural candidate for implementation (TOURISM.WF1). Suppose that we want to carry out a counterfactual analysis to estimate the potential loss of visitors to Turkey in 2020 due to the COVID19 pandemic. First, set the training sample to cover the period until the end of 2019.










Files
References
 Box, G.E.P., and Cox, D.R. (1964), "An analysis of transformations", Journal of the Royal Statistical Society, Series B, vol. 26, no. 2, pp. 211246.
 Guerrero V.M. (1993), "Timeseries analysis supported by power transformations", Journal of Forecasting, vol. 12, pp. 3748.
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