AR(1) Model

# Autoregressive Time Series Modeling

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham

This site provides the necessary tools for the identification, estimation, and forecasting based on autoregressive order one obtained from a given time series:

X(t +1) = F0 + F1X(t) + et,

where et is a White-Noise series. Note that, the

Stationary Condition: | F1| < 1

is expressed as a null hypothesis H0 and being tested.

Notice: As always, it is necessary to construct the graph and , compute statistics and check for both stationary in mean and variance, as well as the seasonality test. For many time-series one must perform, differencing; data transformation; and/or deasonalitization prior to using this JavaScript.

Enter your up-to-84, ordered values of your time series, row-wise and, then click the Calculate button. Blank boxes are not included in the calculations but zeros are.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 X(t) t 15 16 17 18 19 20 21 22 23 24 25 26 27 28 X(t) t 29 30 31 32 33 34 35 36 37 38 39 40 41 42 X(t) t 43 44 45 46 47 48 49 50 51 52 53 54 55 56 X(t) t 57 58 59 60 61 62 63 64 65 66 67 68 69 70 X(t) t 71 72 73 74 75 76 77 78 79 80 81 82 83 84 X(t) Mean X(t) Variance X(t) Autorrelation Its Standard Error Parameter F1 Its Standard Error Parameter F0 Its Standard Error H0: Stationary Condition: | F1| < 1

 White Noise Analysis and Diagnostic Tools Mean Variance Mean: The first half Mean: The second half Variance: The first-half Variance: The second half First order serial-correlation Second order serial-correlation First partial serial-correlation Second partial serial-correlation Durbin-Watson statistic Mean absolute noise Normality Condition ith White Noise ith Step Ahead Forecast

For Technical Details, Back to:
Decision Making in Economics and Finance

Professor Hossein Arsham

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