Unofficial Cheat Sheet for Forecasting

Unofficial Cheat Sheet for Forecasting Forecasting Step 1: Identify stationary or nonstationary Determine trend and seasonality in the t ime series 

Has neither trend nor seasonality  stationary

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Has either trend or seasonality  nonstationary

Identify trend: 1. 2. 3. 4. 5.

a time series plot that is trending up, down, or in a deterministic fashion a highly significant ACF, PACF, and IACF at lag 1 an ACF with many significant lags decaying slowly from lag 1 an ACF with few significant values after first differencing is applied unit root tests that are not significant but become significant when a first difference is applied

Identify seasonality: 1. 2. 3. 4. 5.

a time series plot that has repetitive behavior every S time units significant ACF, PACF, and IACF values at lag S an ACF with significant values at lags that are multiples of S an ACF without a significant value at lag S after a difference of o f order S has been applied seasonal unit root tests that are not significant but become significant when a difference of order S is applied

Step 2: Identify values of p and q: Step 2a: If stationary, identify p and q: 1. Find q such that ACF(q) falls outside confidence limits and ACF(k) falls inside confidence limits for all k>q 2. Find p such that PACF(p) falls outside confidence limits and PACF(k) falls inside confidence limits for all k>p. 3. Determine all ordered pairs (j,k) such that 0≤ j≤p and 0≤k≤q

Step 2b: If nonstationary, detrend and deseasonality: 1. Diagnose trend and seasonality. se asonality. 2. Determine appropriate trend and/or seasonal components to use for modeling. 3. Obtain the residuals (prediction errors) after applying the trend and/or seasonal components. 4. Verify that the residuals appear to be stationary. 5. Use the methods of the previous step 2a to determine an appropriate ARMA model for the residual series. NOTE:

This can also be realized by applying first/seasonal difference

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Step 3: Intervention & Regressors: 

Regressors: Based on the domain knowledge

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Intervention: Identify abnormalities (dips or spikes) in data

Step 4: Combine all the components together (if any) 

ARMA

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Trend: e.g. Linear model, Quadratic, I=1

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Seasonal: e.g. Seasonal dummies

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Trend + Seasonal: e.g. Linear + seasonal dummies, ARIMA

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Interventions and regressors

Step 5: Evaluate models Basically, you are supposed to evaluate and explain the following factors (trade-off): 1. 2. 3. 4. 5.

Whether the model passes all the tests (white noise test, unit root test, seasonal root test) Whether the model has acceptable error (e.g. RMSE) Whether the parameters are significant Whether the model is too complex Whether the forecast is reasonable

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