ARIMAARIMA is part of:
Easy and user-friendly
Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
Data and results shared seamlessly
Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
Accessible - Available in many languages
Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
Automatable and customizable
Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.
XLSTAT-Time 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).
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.
The mathematical writing of the ARIMA models differs from one author to the other. The differences concern most of the time the sign of the coefficients. XLSTAT is using the most commonly found writing, used by most software. If we define by Xt a series with mean µ, then if the series is supposed to follow an ARIMA(p,d,q)(P,D,Q)s model, we can write:
[ Yt = (1 – B)d (1 – Bs)D Xt - µ ; Φ(B)Ø(Bs))Yt = θ(B) Θ(Bs) Zt, Zt∞N(0,σ2) ]
[ Φ(z) = 1 – Σpi=1 Φi zi, Ø(z)= 1 – Σpi=1 Øi zi ; θ(z) = 1 + Σqi=1 θi zi, Θ(z) = 1 + Σqi=1 Θi zi ]
p is the order of the autoregressive part of the model. q is the order of the moving average part of the model. d is the differencing order of the model. D is the differencing order of the 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). P is the order of the autoregressive seasonal part of the model. Q is the order of the moving average seasonal part of the model.
- Remark 1: the Yt process is causal if and only if for any z such that |z|≤1, f(z)≠0 and q(z)≠0.
- Remark 2: if D=0, the model is an ARIMA(p,d,q) model. In that case, P, Q and s are considered as null.
- Remark 3: if d=0 and D=0, the model simplifies to an ARMA(p,q) model.
- Remark 4: if d=0, D=0 and q=0, the model simplifies to an AR(p) model.
- Remark 5: if d=0, D=0 and p=0, the model simplifies to an MA(q) model.
XLSTAT allows you to take into account explanatory variables through a linear model. Three different approaches are possible:
- OLS: A linear regression model is fitted using the classical linear regression approach, then the residuals are modeled using an (S)ARIMA model.
- 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.
- 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.
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.
- Fitting a Holt-Winters seasonal multiplicative model to a time series in XLSTAT
- Fitting an ARIMA model to a time series with XLSTAT-Time
- Running a unit root (Dickey-Fuller) and stationarity test on a time series with XLSTAT