Random Walk Model

The random walk model can also be viewed as an important special case of an ARIMA model (“autoregressive integrated moving average”). Specifically, it is an “ARIMA(0,1,0)” model. More general ARIMA models are capable of dealing with more interesting time patterns that involve correlated steps, such as mean reversion, oscillation, time-varying means, and seasonality.

Ŷt = Yt-1 + α.

Regressive x(t) = alpha * x(t – 1) + error (t)
Moving Average x(t) = beta * error(t-1) + error (t)

Stationarity of Process
Statistical Properties such as mean , variance and autocorrelation are constant over time) is evaluated using AugmentedDickey–Fuller (Unit root test)    

•DataPreprocessing

SeasonalDecomposition is done  and outliers areremoved form residual component.

X(t)= Cycle(Seasonality)+Trend(Shift In Mean)+Residual

Values above 95% quantile range and lower than 5% quantile range are replaced with the respective values.

Holiday Factor Adjustment is done.

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Good company in a journey makes the way seem shorter. — Izaak Walton