Time Series Econometrics Exercises

I have written this code as part of an assignment submission in the course Time Series Econometrics for Finance. This repository conducts analysis and calculations, and creates figures and tables for the hand-in. The repository can be run from the project entry point 00_run_all.R.

Unit-root testing

From Nelson_Plosser_data.xlsx I have focused on the CPI series and tested it for unit roots with the Augmented Dickey-Fuller test.

• 01_empirical_plot_series.R exports a plot with all series in the data and exports all data to a csv file.
• 02_empirical_transform_series.R log-transforms the CPI series, exports a plot of the transformed series, and exports a table with the series and dates.
• 03_empirical_unit_root_testing.R performs the Augmented Dickey-Fuller test, taking to account that the series is trending and thus tests for joint significance of a unit root and a linear time trend. The script exports a latex table with the results.

Estimations on simulated random walks

04_simulated_random_walk_estimation.R simulates $N=100000$ sequences of the pure random walk process

• $x_t = x_{t-1} + u_t$

of size $T=81$ where $u_t \sim N(0,1)$ and $x_0=0$.

It then estimates 3 different linear regression models to the sequences:

1. $x_t = \rho x_{t-1} + u_t$
2. $x_t = c + \rho x_{t-1} + u_t$
3. $x_t = c + \delta t + \rho x_{t-1} + u_t$

where $t$ is a linear and deterministic time trend. The estimates, $\hat \rho$, and the standard errors, $SE(\hat \rho)$, are extracted into a large data table which is then exported in order to avoid to have to redo the simulation for analysis.

05_simulated_random_walk_analysis.R computes t-statistics for the null hypothesis: $\rho=1$ for all series and models. It then calculates percentiles for the 3 different models and exports a latex table, presenting the percentiles per model. It also produces density plots of the t-statistics and estimates and exports those in a joint figure.

NB! The project entry point will look for the simulated data and avoid running the simulation if the data already exists.

US real GDP decompositions

• 06_us_gdp_data.R truncates the US real GDP series from real_gdp_US_2022Q4.xlsx to end at 2019:Q4, log-transforms the series and exports the table.
• 07_us_gdp_decompositions.R applies a Beveridge-Nelson decomposition and a Hodrick-Prescott filter on the real GDP series. It then exports a plot of the transitory components from both decompositions.

The functions that perform the decompositions are defined in src/lib/functions.R.