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Chapter 10 - Time-series analysis. This chapter introduces time series as a concept, and the basic autoregressive process makes it easy to see where the correlation of the error terms can be a problem; discuss the factors affecting the choice between a linear trend and a log-linear trend model for a time series incorporating a trend; | Time-series analysis Basic time series Data on the outcome of a variable or variables in different time periods are known as time-series data. Time-series data are prevalent in finance and can be particularly challenging because they are likely to violate the underlying assumptions of linear regression. Residual errors are correlated instead of being uncorrelated, leading to inconsistent coefficient estimates. The mean and/or variance of the explanatory variables may change over time, leading to invalid regression results. Example of a basic time series known as an autoregressive process: 2 This slide introduces time series as a concept, and the basic autoregressive process makes it easy to see where the correlation of the error terms can be a problem. If we are using time-series observations on a given variable, x, then observations in two or more periods are likely to be related to observations from the prior period purely by construction (they may not be so but are likely to be so) | Time-series analysis Basic time series Data on the outcome of a variable or variables in different time periods are known as time-series data. Time-series data are prevalent in finance and can be particularly challenging because they are likely to violate the underlying assumptions of linear regression. Residual errors are correlated instead of being uncorrelated, leading to inconsistent coefficient estimates. The mean and/or variance of the explanatory variables may change over time, leading to invalid regression results. Example of a basic time series known as an autoregressive process: 2 This slide introduces time series as a concept, and the basic autoregressive process makes it easy to see where the correlation of the error terms can be a problem. If we are using time-series observations on a given variable, x, then observations in two or more periods are likely to be related to observations from the prior period purely by construction (they may not be so but are likely to be so) as seen in the autoregressive process in the slide. 2 Trend analysis The most basic form of time-series analysis examines trends that are sustained movements in the variable of interest in a specific direction. Trend analysis often takes one of two forms: Linear trend analysis, in which the dependent variable changes at a constant rate over time. Ex: if b0=3 and b1=2.3, then the predicted value of y after three periods is 2. Log-linear trend analysis, in which the dependent variable changes at an exponential rate over time or constant growth at a particular rate Ex: if b0=2.8 and b1=1.4, then the predicted value of y after three periods is 3 LOS: Compute the predicted trend value for a time series modeled as either a linear trend or log-linear trend, given the estimated trend coefficients. Pages 377–381 Recall that the inverse process of ln() is raising e to the () power. Because it is the slope of the trend line, b1 is referred to as the trend coefficient. Log-linear growth should be
