3.
Data Trend Model Seasonality Log-Linear Model Linear Model Auto-Regressive Model Regression Analysis Cross-sectional Data Time dependent Data Significant Autocorrelation among Residuals Yes No Significant Autocorrelation among Residuals Significant Autocorrelation among lagged residuals Yes Yes No No Make a Graph Correctly Specified Model
12.
Data Trend Model Seasonality Log-Linear Model Linear Model Auto-Regressive Model Regression Analysis Cross-sectional Data Time dependent Data Significant Autocorrelation among Residuals Yes No Significant Autocorrelation among Residuals Significant Autocorrelation among lagged residuals Yes Yes No No Make a Graph Correctly Specified Model
Time Series is a series of the variable values taken at equal interval of time. The closing price of the IBM stock observed for 10 years constitutes the time series of the IBM stock price.
Time series may have a pattern when plotted against the time, which depicts the characteristics of the IBM stock and the capital markets in general.
These patterns in the stock price time series are called trends in the time series,
An American retail chain (AMR) which sells woolen clothes, will have increased sales pattern in the winters and a moderate sales in the summer.
The quarterly sales of AMR when plotted against the time for 4 years will show moderate sales in summers and increased sales in winters
The above shown trends in the sales are called seasonal trends
The most important assumption of the linear regression is that the error terms are not correlated with each other.
Other important assumption of the linear regression is that the residual term is independently distributed.
These two important assumptions when violated becomes the limitation for the trend models as linear regression is used in trend models.
To overcome the autocorrelation problem(violation of independent and uncorrelated residuals assumption), log-linear trend model can be used which reduces the serial correlation.
After applying the log-linear trend model, the serial correlation may persist, which means even a log-linear trend model is inappropriate for the case. This hints us to use some other form model which are autoregressive models.
In Autoregressive(AR) models, the dependent variable is regressed with its lagged term.
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