GAUSS arimaPredict Example

Introduction

This example estimates and predicts an AR(2) model in GAUSS using simulated data. It demonstrates usage of arimaFit, arimaPredict and simarmamt.

Simulate Data

The GAUSS function simarmamt allows users to randomly generate ARMA data based on user-input data characteristics. This example simulates a series using the data generation process given by

$$z_{t} = 0.3z_{t-1} + \epsilon_{t}$$

// Simulate arima data
seed = 423458;
y = simarmamt(.3, 1, 0, 2, 0, 250, 1, .5, seed);

// Integrate the series
z = cumsumc(y);

Estimate the Model

This example estimates the parameters of an AR(2) model from the simulated data using the GAUSS arimaFit procedure.

// Initialize arimaOut structure
struct arimamtOut amo;

// Set AR order
p = 1;

// Run with differencing
d = 1;

// Run arima estimation
amo = arimaFit(z, p, d);

Estimation Output

The output from the model estimation reads:

Final Results:

Log Likelihood:    934.057412         Number of Residuals: 249
AIC : -1866.114824 Error Variance : 1.158524598
SBC : -1862.597371 Standard Error : 1.076347805
DF: 248 SSE: 287.314100182
Coefficients Std. Err. T-Ratio Approx. Prob. AR[1,1] 0.32317 0.06046 5.34534 0.00000
Constant: 1.24951510 Total Computation Time: 0.59 (seconds) AR Roots and Moduli: Real : 3.09431 Imag.: 0.00000 Mod. : 3.09431

Predict Model

The final step is to predict the model using arimaPredict

// Forecast 25 periods
f = arimaPredict(amo, z, 25);

Prediction Output

The output from this final step reads:

Forecasts for ARIMA(1,1,0) Model.   95% Confidence Interval Computed.

 Period        LCL        Forecasts        UCL     Forecast Std. Err.
   251    459.825730    461.939599    464.053468      1.078524
   252    459.553388    463.059347    466.565305      1.788787
   253    459.641039    464.266924    468.892810      2.360189
   254    459.940368    465.502886    471.065404      2.838072
   255    460.374059    466.748021    473.121984      3.252081
   256    460.899670    467.996121    475.092572      3.620705
   257    461.492316    469.245178    476.998041      3.955615
   258    462.136376    470.494546    478.852715      4.264451
   259    462.821419    471.744013    480.666607      4.552428
   260    463.540107    472.993513    482.446918      4.823255
   261    464.287058    474.243023    484.198987      5.079667
   262    465.058187    475.492536    485.926886      5.323746
   263    465.850307    476.742051    487.633794      5.557114
   264    466.660877    477.991566    489.322255      5.781070
   265    467.487828    479.241081    490.994333      5.996668
   266    468.329454    480.490596    492.651738      6.204779
   267    469.184323    481.740111    494.295899      6.406132
   268    470.051224    482.989626    495.928028      6.601347
   269    470.929119    484.239141    497.549163      6.790953
   270    471.817112    485.488656    499.160201      6.975406
   271    472.714421    486.738171    500.761921      7.155106
   272    473.620362    487.987686    502.355011      7.330402
   273    474.534330    489.237202    503.940073      7.501603
   274    475.455786    490.486717    505.517647      7.668983
   275    476.384251    491.736232    507.088213      7.832788

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