Statistical details explained

A forecasting run generates forecasts and forecasting statistical details. Forecasting statistical details are located in the Statistical details tab on the Forecasting preview.

Forecast detailed information contains forecast Accuracy details, Parameters, Statistical model, and Trend and Seasonality.

Prediction accuracy

Accuracy details (1)

Model accuracy is based on the historical data of the time series data that is used to generate the model. Accuracy details can also be used as an indicator of the forecast accuracy, but they do not carry over to future values.

Akaike Information Criterion (AIC)
A model selection measure. The AIC penalizes models with many parameters, and so attempts to choose the best model with a preference towards simpler models. The AIC is the sum of the logarithm of non-adjusted MSE multiplied by the number of historical points and the number of model parameters and initial smoothing states that are multiplied by 2.
Mean Absolute Error (MAE)
Computed as the average absolute difference between the values fitted by the model (one-step ahead in-sample forecast), and the observed historical data.
Mean Absolute Percent Error (MAPE)
The average absolute percent difference between the values that are fitted by the model and the observed data values.
Mean Absolute Scaled Error (MASE)
The error measure that is used for model accuracy. It is the MAE divided by the MAE of the naive model. The naive model is one that predicts the value at time point t as the previous historical value. Scaling by this error means that you can evaluate how good the model is compared to the naive model. If the MASE is greater than 1, then the model is worse than the naive model. The lower the MASE, the better the model is compared to the naive model.
Root Mean Squared Error (RMSE)

The square root of the MSE. It is on the same scale as the observed data values. Mean Squared Error (MSE): The sum of squared difference between the values that are fitted by the model and observed values that are divided by the number of historical points, minus the number of parameters in the model. The number of parameters in the model is subtracted from the number of historical points to be consistent with an unbiased model variance estimate.

Mean Squared Error (MSE)
The sum of squared difference between the values that are fitted by the model, and observed values that are divided by the number of historical points, minus the number of parameters in the model. The number of parameters in the model is subtracted from the number of historical points to be consistent with an unbiased model variance estimate.

Parameters (2)

Detected Seasonal period and estimates for other parameters that are used in the selected exponential smoothing model are available.

Alpha
The smoothing factor for level states in the exponential smoothing model. Small values of alpha increase the amount of smoothing, that is, more history is considered when the alpha is small. Large values of alpha reduce the amount of smoothing, which means that more weight is placed on the more recent observations. When the alpha is 1, all the weight is placed on the current observation.
Beta
The smoothing factor for trend states in the exponential smoothing model. This parameter behaves similar to alpha, but is for trend instead of level states.
Gamma
The smoothing factor for seasonality states in the exponential smoothing model. Serves the similar role as alpha, but for the seasonal component of the model.
Phi
The damping coefficient in the exponential smoothing model. Long forecasts can lead to unrealistic results, and it is useful to have a damping factor to dampen the trend over time and produce more conservative forecasts.

Statistical model (3)

Forecasting uses exponential smoothing. Every exponential smoothing model that is fit contains a level component. However, trend and seasonal components are not always present. The following table shows the different types of exponential smoothing models that are fit and accompanying time series data examples for each model type.

Trend component Seasonal component
 

None

Additive

Multiplicative

None

Simple exponential smoothing

Simple exponential smoothing

 

Additive

Holt’s linear method

Additive Holt-Winters’ method

Multiplicative Holt-Winters’ method

Additive damped

Additive damped trend method

Additive Holt-Winters’ method with damped trend

Multiplicative Holt-Winters’ method with damped trend

The following diagram illustrates what the detected model might be with the given historical data (blue) and the resulting forecasting data (yellow).

Detected forecasting model

Time series data that contains a trend, for example, slope, can be modeled with a trend component. The trend can be damped or non-damped. Damped trend eventually levels off into a flat line, which leads to a more conservative fit while undamped would continue to grow without bounds.

Time series data that contains regularly repeating cycles, can be modeled with a seasonal component. The seasonality can be additive or multiplicative. An example of multiplicative seasonality is an amplitude that is constantly growing or shrinking with time. If the seasonal pattern is constant, then additive seasonality is used.

Trend component

Identifies the trend component. Supported types include: None (trend not detected), Additive and Additive damped.

Seasonality component

Identifies the seasonality component. Supported types include: None (seasonality not detected), Additive and Multiplicative.

Trend and seasonality (4)

Trend strength

Compare the original model, M, and the same model with the trend component removed. The trend strength of M is the difference in accuracy between model M and model M with the trend component removed.

Seasonality strength

Compare the original model, M, and the same model with the seasonal component removed. The seasonality strength of M is the difference in accuracy between model M and model M with the seasonal component removed.

Seasonality period

The number of contiguous items detected per cycle. For example, if the finest granularity of the time series is months, then a number of 12 here would represent an expectation that a repeating pattern yearly exists.