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Stationarity Stationarity impacts our ability to model and forecast  A stationary series has the same mean and variance over time  Non-stationary series are much harder to model  Common approach:  Identify sources of non-stationarity  Transform series to make it stationary  Build models with stationary series  The Augmented Dickey-Fuller (ADF) test specifically tests for stationarity.  It is a hypothesis test: the test returns a p-value,  and we generally say the series is non-stationary if the p-value is less than 0.05.  It is a less appropriate test to use with small datasets,  or data with heteroscedasticity (different variance across observations) present.  It is best to pair ADF with other techniques such as:  run-sequence plots, summary statistics, or histograms.   Common Transformations for Time Series include:  Transformations allow us to generate stationary inputs required by most models.  There are several ways to transform nonstationary time series data:  Remove trend (constant mean)  Remove heteroscedasticity with log (constant variance)  Remove autocorrelation with differencing (exploit constant structure)  Remove seasonality (no periodic component)  Multiple transformations are often required.   Time Series Smoothing Smoothing is a process that often improves our ability to forecast series by reducing the impact of noise.  There are many ways to smooth data. Some examples:  Simple average smoothing  Equally weighted moving average  Exponentially weighted moving average  This are some suggestions for selecting a Smoothing Technique. If your data:  –       lack a trend Then use Single Exponential Smoothing  –       have trend but no seasonality Then use Double Exponential Smoothing  –       have trend and seasonality Then use Triple Exponential Smoothing

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