# Time Series Analysis Definition of a Time Series process

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Time Series Analysis Definition of a Time Series process
AR, MA, ARMA, ARIMA Vector Autoregression Impulse Response Forecasting

Four Components of a Time Series
Trend Season Cycle Random (refer STAMP manual p.140)

Iterative Substitution in AR(1) Model

AR(1) Time Series as a Function of Past Innovations (Impulses or Shocks)

Time Dependent Variance

Dicky-Fuller and Augmented Dicky-Fuller Tests
Null hypotheses: There is unit root and time series in non-stationary =0  (1-)=0 Alternative hypothesis: There is no unit root and time series is stationary <0  (1-)<0  <1

Moving Average-MA Process

MA(2) Process

Autoregressive Process

ARMA(1,1) Process

Co-integration

Error Correction Model

Structure of a VAR Model
. Simple Example

Impulse Response Analysis in a VAR Model

Stamp Program for Time Series Analysis
Estimation sample is (T = 116, n = 111). Log-Likelihood is (-2 LogL = ). Prediction error variance is Summary statistics ER Std.Error Normality H( 37) r( 1) r( 9) DW Q( 9, 6) Rs^ ER = Trend + Trigo seasonal + Expl vars + Irregular Eq 3 : Estimated coefficients of final state vector. Variable Coefficient R.m.s.e t-value Lvl [ ] Slp [ ] Sea_ [ ] Sea_ [ ] Sea_ [ ] Eq 3 : Estimated coefficients of explanatory variables. ER_ [ ] ER_ [ ] ER_ [ ] ER_ [ ] Eq 3 : Seasonal analysis (at end of period). Seasonal Chi^2( 3) test is [0.9818]. Seas Seas Seas Seas 4 Value

Forecasting of the Exchange Rate

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