How to choose forecasting models

Steps in choosing a forecasting model
Forecasting flow chart
Data transformations and forecasting models: what to use and when
Automatic forecasting software
Political and ethical issues in forecasting
How to avoid trouble: principles of good data analysis

Data transformations and forecasting models: what to use and when

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Transformation Properties  When to use  Points to keep in mind   
 
 
Deflation by Converts data from  When data are measured To generate a true forecast for the future 
CPI or nominal dollars (or in nominal dollars (or in nominal terms, you will need to make an 
another price other currency) to other currency) and you explicit forecast of the future value of the 
index constant dollars; want to explicitly show price index--i.e., you will need to forecast 
 usually helps to the effect of the inflation rate (but this is easy if  
 stablilize variance inflation--i.e., uncover you're in a period of steady inflation) 
 "real growth" 
 
Deflation at Merely applies a  When you only need to When used with a zero-trend model like 
a fixed rate constant discount approximately model the simple exponential smoothing or random walk 
 factor to past data effect of past inflation without growth, the assumed inflation rate 
 and/or you wish to is precisely the percentage growth in the 
 impose an assumption future forecasts.  
 about the current and 
 future inflation 
  rate--you can twiddle 
 the inflation rate to 
 see what value does the  
 best job of flattening 
 out the trend and/or  
 stabilizing the variance 
 
Logarithm Converts When compound growth is Logging is not the same as deflating: it 
 multiplicative not due to inflation linearizes growth but does not remove a 
 patterns to additive (e.g. when data is not general upward trend; if logged data still 
 patterns and/or measured in currency); have a consistent upward trend, then you 
 linearizes when you do not need to should use a model that includes a trend 
 exponential growth; separate inflation from factor (e.g., random walk with growth, 
 converts absolute real growth; when data ARIMA, linear exponential smoothing). 
 changes to distribution is positive 
 percentage changes; and highly skewed (e.g., 
 often stablizes the exponential or 
 variance of data log-normal  
 with compound distribution); when 
 growth, regardless variables are  
 of whether deflation multiplicatively related 
 is also used 
 
First Converts "levels" to When you need to Differencing is an explicit option in ARIMA 
difference "changes" stationarize a series modeling and it is implicitly a part of 
 with a strong trend random walk and exponential smoothing 
 and/or random-walk  models; therefore you would not manually 
 behavior (often useful difference the input variable (using the 
 when fitting regression DIFF function) when specifying model type as 
 models to time series "random walk" or "exponential smoothing" or 
 data) "ARIMA"; first difference of LOG(Y) is the
  percentage change in Y
 
Seasonal Converts "levels" to When you need to remove Seasonal differencing is an explicit option 
difference "seasonal changes" the gross features of in ARIMA modeling; you MUST include a 
 seasonality from a seasonal difference (as a modeling option, 
 strongly seasonal series not an SDIFF transformation of the input 
 without going to the variable) if the seasonal pattern is 
 trouble of estimating consistent and you wish it to be maintained 
  seasonal indices in long-term forecasts 
 
Seasonal Removes a constant When you wish to Adds a lot of parameters to the model--one 
adjustment seasonal pattern separate out the  for each season of the year. 
 from a series seasonal component of a (In Statgraphics, the seasonal indices 
 (either series and then fit are not explicitly shown in the output  
 multiplicative or what's left with a of the Forecasting procedure--you must
 additive) nonseasonal model separately run the Descriptive Methods 
 (regression, smoothing, procedure to display the seasonal indices.) or trend line); normally 
 use the multiplicative  
 version unless data has 
 been logged 
 
 

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Model type  Properties  When to use  Points to keep in mind   
 
Random walk Predicts that "next As a baseline against Plot of forecasts looks exactly like a plot 
 period equals this which to compare more of the data, except lagged by one period 
  period" (perhaps elaborate models; when (and shifted slightly up or down if a growth 
 plus a constant); applied to logged data, term is included); long term forecasts 
 a.k.a. ARIMA(0,1,0) it is a "geometric" follow a straight line (horizontal if no 
 model random walk--the default growth term is included); confidence 
 model for stock market intervals for long-term forecasts widen 
 data according to a square-root law (sideways- 
 parabola shape); logically equivalent to 
  MEAN model fitted to DIFF(Y) 
 
Linear trend Regression of Y on Rarely the best model Forecasts follow a straight line whose slope 
 the time index for forecasting--use equals the average slope over the whole 
 only when you have very estimation period but whose intercept is 
 few data points and no anchored in the distant past; short-term 
 obvious pattern in data forecasts therefore may miss badly and 
 other than a slight confidence intervals for long-term forecasts 
  trend; can be used in are usually not reliable; other models that 
 conjunction with extrapolate a linear trend into the future 
 seasonal adjustment--but (random walk with growth, linear exponential 
 if you have enough data smoothing, ARIMA models with 1 
 to seasonally adjust, difference w/constant or 2 differences w/o 
 you probably should use constant) often do a better job by 
 another model "reanchoring" the trend line on recent data 
 
Simple moving Simple (equally When data are in short Primitive but relatively robust against 
average weighted) average of supply and/or highly outliers and messy data; long-term forecasts 
 recent data irregular are a horizontal line extrapolated from the 
 most recent average; a long-term trend can 
 be incorporated via fixed-rate deflation at 
 an assumed interest rate 
 
Simple Exponentially When data are nonseasonal Long-term forecasts are a horizontal line 
exponential weighted average of (or deseasonalized) and extrapolated from the most recent smoothed 
smoothing recent data; display a time-varying value; same as a random walk model without 
 "average age" of  mean without a growth if alpha=0.9999; forecasts get 
 data in forecast consistent trend smoother and slower to respond to turning 
 (amount by which points as alpha approaches zero; confidence 
 forecasts lag behind intervals widen less rapidly than in the 
 turning points) is random walk model; a long-term trend can be 
 1/alpha; same as an incorporated via fixed-rate deflation at an 
 ARIMA(0,1,1) model assumed interest rate or by fitting an 
 without constant  ARIMA(0,1,1) model with constant 
 
Linear Assumes a When data are nonseasonal Long-term forecasts follow a straight line 
exponential time-varying linear (or deseasonalized) and whose slope is the estimated local trend at 
smoothing trend as well as a display time-varying the end of the series; confidence intervals 
(Brown's or time-varying level local trends (usually for long-term forecasts widen rapidly--the  
Holt's) (Brown's uses 1 applicable to data that model assumes that the future is VERY 
 parameter, Holt's are "smoother" in uncertain because of time-varying trends; 
 uses separate  appearance--i.e., less often does not outperform simple exponential 
 smoothing parameters noisy--than what would smoothing, even for data with trends, 
 for level and be well fitted by simple because extrapolation of time-varying trends 
 trend); essentially exponential smoothing) is risky 
 an ARIMA(0,2,2)  
 model without 
 constant 
 
Seasonal Predicts that "next As a baseline against Long-term forecasts have same seasonal 
random walk period equals same which to compare fancier pattern as last year; long-term trend is 
 period last year" seasonal models; as equal to the average trend over whole past 
 (plus constant); an foundation for seasonal history of series; confidence intervals 
 ARIMA(0,0,0)x(0,1,0) ARIMA models (e.g., widen slowly; slow to respond to cyclical 
 model with constant (1,0,0)x(0,1,1)) upturns and downturns; logically equivalent 
 to MEAN model fitted to SDIFF(Y,s) 
 
Seasonal Predicts that change As a baseline against Long-term forecasts have same seasonal 
random trend from this period to which to compare fancier pattern as last year; long-term trend is 
 next period will be seasonal models; as  equal to the most recently observed annual 
 the same as change foundation for seasonal trend; confidence intervals widen rapidly; 
 observed at this ARIMA models (e.g., quick to respond to cyclical upturns and 
 time last year; an (0,1,1)x(0,1,1) without downturns; logically equivalent to MEAN 
 ARIMA(0,1,0) constant) model fitted to DIFF(SDIFF(Y)) (with no 
 x(0,1,0) model constant--i.e., mean is assumed to be zero) 
 without constant 
 
Winter's Assumes time-varying When data are trended and Initialization of seasonal indices and joint 
seasonal level, trend, and seasonal and you wish to estimation of three smoothing parameters is 
smoothing seasonal indices decompose it into local sometimes tricky--watch to see that 
 (either level/trend/seasonal parameter estimates converge and that 
 multiplicative or factors; normally you forecasts and confidence intervals look 
 additive use the multiplicative reasonable; a popular choice for "automatic" 
 seasonality) version unless data is forecasting because it does a little of 
 logged  everything, but has a lot of parameters and 
 sometimes overfits the data or is unstable 
 
Multiple A general linear When data are Forecasts cannot be extrapolated into the 
regression forecasting equation correlated with other future unless and until values are available 
 involving other explanatory or causal for the independent variables; for this 
  variables variables (e.g., price, reason the independent variables must often 
 advertising, promotions, be lagged by one or more periods--but when 
 interest rates, only lagged variables are used, a regression 
 indicators of general model may fail to outperform a time series 
 economic activity, model which relies only on the history of 
 etc.); the key is to the original series; regressions of 
 choose the right nonstationary variables often have high 
  variables and the right "R-squared" but poor performance compared to 
 transformations of those time series models; it often helps to 
 variables to justify the stationarize the dependent variable and/or 
 assumption of a linear add lags of the dependent and independent 
 model and to take into variables to the model; "automatic" model 
 account the time selection techniques such as stepwise 
 dimension in the data regression and all-possible regressions are 
  available, but beware of overfitting; it is 
 important to validate the model by testing 
  it on hold-out data and by computing its 
 "effective R-squared" (percent of variance 
 explained) relative to a random walk model 
 or other appropriate time series model 
 
ARIMA A general class of When data are relatively ARIMA models are designed to squeeze all 
  models that includes plentiful (4 seasons or autocorrelation out of the original time 
 random walk, random more) and can be series; a systematic procedure exists for 
 trend, seasonal and satisfactorily identifying the best ARIMA model for any 
 non-seasonal stationarized by given time series; features of ARIMA 
 exponential differencing and other and multiple regression models can be 
 smoothing, and auto- mathematical combined in a natural way; ARIMA models 
 regressive models; transformations; when it often provide a good fit to highly 
 forecasts for the is not necessary to aggregated, highly plentiful data; they may 
 stationarized explicitly separate out perform relatively less well on 
 dependent variable the seasonal component disaggregated, irregular, and/or sparse data 
 are a linear (if any) in the form of 
 function of lags of seasonal indices  
 the dependent 
 variable and/or lags 
  of the errors 
 

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