Simple AR1 model#


Below is the documentation for the Matlab code in “NNE_AR1” folder at this GitHub repository. The code uses NNE to estimate a simple AR1 model: \(y_{i}={\beta}y_{i-1}+\epsilon_{i}\). This is a toy example where we don’t see computational or accuracy gains from NNE. But the simplicity allows NNE to be easily understood.

Workflow#

The following commands run a Monte Carlo experiment that estimates the AR1 on a simulated dataset.

>> monte_carlo_data         % simulate an AR1 time series and save it in data.mat
>> nne_gen                  % generate the training examples for NNE and save them in nne_training.mat
>> nne_train                % train a neural net and apply it to data.mat

Description of each file#

model.m#

This function codes the simple AR1 model.

y = model(beta)

  • Input beta: the coefficient in the AR1 model.

  • Output y: a vector containing the simulated time series.

moments.m#

This function summarizes data into a set of moment(s).

output = moments(y)

  • Input y: time-series vector as outputted from model.m.

  • Output: the value of the moment(s).

monte_carlo_data.m#

This script creates a time series for Monte Carlo experiment. It uses model.m to simulate the time series under a “true” value of \(\beta\), and then saves the time series into data.mat.

nne_gen.m#

This script generates the training and validation examples.

  • It uses model.m to simulate the time-series data in each training or validation example.

  • It uses moments.m to summarize data in each training or validation example.

  • The training and validation examples are saved to nne_training.mat.

nne_train.m#

This script trains a shallow neural net.

  • It loads the training and validation examples from nne_training.mat (saved by nne_gen.m).

  • Validation loss is reported. We can use this loss to choose neural net hyperparameters (e.g., the number of hidden nodes).

  • It applies the trained neural net to data.mat.