Time Series Analysis: Simple and Log-linear Trend Models

Simple Time Series Models

This is basic trend modeling.

A simple trend model can be expressed as follows:

y~t=b0+b1t+εt\tilde{y}_t = b_0 + b_1 t + \varepsilon_t
  • b0b_0 = the y-intercept; where t = 0.
  • b1b_1 = the slope coefficient of the time trend.
  • t = the time period.
  • y~t\tilde{y}_t = the estimated value for time t based on the model.
  • εt\varepsilon_t = the random error of the time trend.

The big validity pit-fall for simple trend models is serial correlation; if this problem is present, then you will see an artificially high R2 and your slope coefficient may falsely appear to be significant.

There is a visual way to detect serial correlation (not shown) or you can perform a Dubin-Watson test.

Log-linear Trend Models

This applies to non-linear time series trends.

The structure is:

lnyt=b0+b1t+et\ln y_t = b_0 + b_1 t + e_tyt=eb0+b1t+ety_t = e^{b_0 + b_1 t + e_t}

Again, like the simple trend model, use a graph or Durbin Watson test to check for serial correlation, as this will be a big threat to validity.

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Data Science in Finance: 9-Book Bundle

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Master R and Python for financial data science with our comprehensive bundle of 9 ebooks.

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  • Getting Started with R
  • R Programming for Data Science
  • Data Visualization with R
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  • Quantitative Trading Strategies with R
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  • Credit Risk Modelling With R
  • Python for Data Science
  • Machine Learning in Finance using Python

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