#Free forecasting software excel series#

WN variance: The white noise variance is equal to the SSE divided by N.

MAPE: The Mean Absolute Percentage Error measures the quality of the fit, while removing the scale effect and not relatively penalizing bigger errors.

This statistic is minimized if the 'Least Squares' option has been selected for the optimization.

Observations: The number of data used for the fitting of the model.

If initial coefficients have been entered the results corresponding to these coefficients are displayed first. If a preliminary estimation and an optimization have been requested the results for the preliminary estimation are first displayed followed by the results after the optimization. Summary statistics: This table displays for the selected variables, the number of observations, the number of missing values, the number of non- missing values, the mean and the standard deviation (unbiased). Note: if no differencing is requested (d=0 and D=0), and if there are no explanatory variables in the model, the constant of the model is estimated using CO-LS.

GLS: A linear regression model is fitted, then the residuals are modeled using an (S)ARIMA model, then we loop back to the regression step, in order to improve the likelihood of the model by changing the regression coefficients using a Newton-Raphson approach.

CO-LS: If d or D and s are not zero, the data (including the explanatory variables) are differenced, then the corresponding ARMA model is fitted at the same time as the linear model coefficients using the Cochrane and Orcutt (1949) approach.

OLS: A linear regression model is fitted using the classical linear regression approach, then the residuals are modeled using an (S)ARIMA model.

XLSTAT allows you to take into account explanatory variables through a linear model.

Remark 5: if d=0, D=0 and p=0, the model simplifies to an MA(q) model.

Remark 4: if d=0, D=0 and q=0, the model simplifies to an AR(p) model.

Remark 3: if d=0 and D=0, the model simplifies to an ARMA(p,q) model.

In that case, P, Q and s are considered as null.

Remark 2: if D=0, the model is an ARIMA(p,d,q) model.

Remark 1: the Yt process is causal if and only if for any z such that |z|в‰¤1, f(z)в‰ 0 and q(z)в‰ 0.

Q is the order of the moving average seasonal part of the model. P is the order of the autoregressive seasonal part of the model. s is the period of the model (for example 12 if the data are monthly data, and if one noticed a yearly periodicity in the data). D is the differencing order of the seasonal part of the model. d is the differencing order of the model. q is the order of the moving average part of the model. P is the order of the autoregressive part of the model.

#Free forecasting software excel series#

If we define by Xt a series with mean Вµ, then if the series is supposed to follow an ARIMA(p,d,q)(P,D,Q)s model, we can write: XLSTAT is using the most commonly found writing, used by most software.

The differences concern most of the time the sign of the coefficients. The mathematical writing of the ARIMA models differs from one author to the other. The models of the ARIMA family allow to represent in a synthetic way phenomena that vary with time, and to predict future values with a confidence interval around the predictions. XLSTAT offers a wide selection of ARIMA models such as ARMA (Autoregressive Moving Average), ARIMA (Autoregressive Integrated Moving Average) or SARIMA (Seasonal Autoregressive Integrated Moving Average).