# Auto-Regressive (AR) Time Series Models

- Auto-Regressive (AR) Time Series Models
- This type of time series model utilizes a time period lagged observation as the independent variable to predict the dependent variable, which is the value in the next time period.

xt = b0 + b1xt-1 + εt

- There can be more than one time period lag independent variable.
- Valid statistical inferences from AR time series models only if the time series is covariance stationary; a time series with growth over time or seasonality is not covariance stationary.
- It is critical to test your AR time series model for serial correlation and the Durbin-Watson test cannot be used for this model.
- An AR time series model that is covariance stationary will exhibit mean reversion – it will tend to fall after going above the mean and rise after going below the mean.
- Root Mean Square Error (RMSE) = a method of assessing the out of sample accuracy of a time series model’s forecast. If comparing multiple models, the model will the lowest RMSE is considered to have the best forecasting capabilities.

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LESSONS

- CFA L2: Quantitative Methods - Introduction
- Quants: Correlation Analysis
- Quants: Single Variable Linear Regression Analysis
- Standard Error of the Estimate or SEE
- Confidence Intervals (CI) for Dependent Variable Prediction
- Coefficient of Determination (R-Squared)
- Analysis of Variance or ANOVA
- Multiple Regression Analysis
- Multiple Regression and Coefficient of Determination (R-Squared)
- Fcalc – the Global Test for Regression Significance
- Regression Analysis and Assumption Violations
- Qualitative and Dummy Variables in Regression Modeling
- Time Series Analysis: Simple and Log-linear Trend Models
- Auto-Regressive (AR) Time Series Models
- Auto-Regressive Models - Random Walks and Unit Roots
- ARMA Models and ARCH Testing
- How to Select the Most Appropriate Time Series Model?

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