Code for running LSTM neural networks on economic data for nowcasting

## Project description

# nowcast_lstm

**New in v0.2.6**: ability to produce logistic/binary classification estimates by passing `torch.nn.BCELoss()`

to the `criterion`

parameter.

**New in v0.2.2**: ability to get uncertainty intervals for predictions and predictions on synthetic vintages.

**New in v0.2.0**: ability to get feature contributions to the model and perform automatic hyperparameter tuning and variable selection, no need to write this outside of the library anymore.

**Installation**: from the command line run:

```
# you may have pip3 installed, in which case run "pip3 install..."
pip install dill numpy pandas pmdarima
# pytorch has a little more involved install command, this for windows
pip install torch==1.8.1+cpu torchvision==0.9.1+cpu torchaudio===0.8.1 -f https://download.pytorch.org/whl/torch_stable.html
# this for linux
pip install torch==1.8.1+cpu torchvision==0.9.1+cpu torchaudio==0.8.1 -f https://download.pytorch.org/whl/torch_stable.html
# then finally
pip install nowcast-lstm
```

**Example**: `nowcast_lstm_example.zip`

contains a jupyter notebook file with a dataset and more detailed example of usage.

LSTM neural networks have been used for nowcasting before, combining the strengths of artificial neural networks with a temporal aspect. However their use in nowcasting economic indicators remains limited, no doubt in part due to the difficulty of obtaining results in existing deep learning frameworks. This library seeks to streamline the process of obtaining results in the hopes of expanding the domains to which LSTM can be applied.

While neural networks are flexible and this framework may be able to get sensible results on levels, the model architecture was developed to nowcast growth rates of economic indicators. As such training inputs should ideally be stationary and seasonally adjusted.

Further explanation of the background problem can be found in this paper. Further explanation and results can be found in this paper in the Journal of Official Statistics.

## R, MATLAB, and Julia wrappers

R, MATLAB, and Julia wrappers exist for this Python library. Python and some Python libraries still need to be installed on your system, but full functionality from R can be obtained with the wrappers without any Python knowledge. The MATLAB and Julia wrappers work with older versions of the library but are no longer being mantained and updated to work with the newest features.

## Quick usage

The main object and functionality of the library comes from the `LSTM`

object. Given `data`

= a pandas DataFrame of a date column + monthly data + a quarterly target series to run the model on, usage is as follows:

```
from nowcast_lstm.LSTM import LSTM
# note that if a column has no data in it, i.e., is all NAs, its values will be replaced with 0. This won't affect model performance and will ensure that the model can still be trained
# a list of columns with no data in them can be accessed with `model.no_data_cols`
model = LSTM(data, "target_col_name", n_timesteps=12) # default parameters with 12 timestep history
#model = LSTM(data, "target_col_name", n_timesteps=12, n_models=10, seeds=list(range(10)) # For reproducibility on a single machine/system, give a list of manual seeds as long as the n_models parameter. Reproducibility across machines is not guaranteed.
model.X # array of the transformed training dataset
model.y # array of the target values
model.mv_lstm # list of trained PyTorch network(s)
model.train_loss # list of training losses for the network(s)
model.train()
model.predict(model.data) # predictions on the training set
# predicting on a testset, which is the same dataframe as the training data + newer data
# this will give predictions for all dates, but only predictions after the training data ends should be considered for testing
model.predict(test_data)
# to gauge performance on artificial data vintages
model.ragged_preds(pub_lags, lag, test_data)
# save a trained model using dill
import dill
dill.dump(model, open("trained_model.pkl", mode="wb"))
# load a previously trained model using dill
trained_model = dill.load(open("trained_model.pkl", "rb", -1))
```

## Model selection

To ease variable and hyperparameter selection, the library provides provisions for this process to be carried out automatically. See the example file or run `help()`

on the functions for more information.

```
from nowcast_lstm.model_selection import variable_selection, hyperparameter_tuning, select_model
# case where given hyperparameters, want to select which variables go into the model
selected_variables = variable_selection(data, "target_col_name", n_timesteps=12) # default parameters with 12 timestep history
# case where given variables, want to select hyperparameters
performance = hyperparameter_tuning(data, "target_col_name", n_timesteps_grid=[12], n_hidden_grid=[10,20])
# case where want to select both variables and hyperparameters for the model
performance = select_model(data, "target_col_name", n_timesteps_grid=[12], n_hidden_grid=[10,20])
```

## Prediction uncertainty

Produce estimates along with lower and upper bounds of an uncertainty interval. See the example Jupyter Notebook for more information on the methodology employed.

```
from nowcast_lstm.LSTM import LSTM
# where model = a trained model
model.interval_predict(
test_data,
interval = 0.95 # float from 0 to 1, how large to make intervals (higher = larger)
)
# predictions on synthetic vintages
model.ragged_interval_predict(
pub_lags,
lag,
test_data,
interval = 0.95
)
```

## LSTM parameters

`data`

:`pandas DataFrame`

of the data to train the model on. Should contain a target column. Any non-numeric columns will be dropped. It should be in the most frequent period of the data. E.g. if I have three monthly variables, two quarterly variables, and a quarterly series, the rows of the dataframe should be months, with the quarterly values appearing every three months (whether Q1 = Jan 1 or Mar 1 depends on the series, but generally the quarterly value should come at the end of the quarter, i.e. Mar 1), with NAs or 0s in between. The same logic applies for yearly variables.`target_variable`

: a`string`

, the name of the target column in the dataframe.`n_timesteps`

: an`int`

, corresponding to the "memory" of the network, i.e. the target value depends on the x past values of the independent variables. For example, if the data is monthly,`n_timesteps=12`

means that the estimated target value is based on the previous years' worth of data, 24 is the last two years', etc. This is a hyper parameter that can be evaluated.`fill_na_func`

: a function used to replace missing values. Should take a column as a parameter and return a scalar, e.g.`np.nanmean`

or`np.nanmedian`

.`fill_ragged_edges_func`

: a function used to replace missing values at the end of series. Leave blank to use the same function as`fill_na_func`

, pass`"ARMA"`

to use ARMA estimation using`pmdarima.arima.auto_arima`

.`n_models`

:`int`

of the number of networks to train and predict on. Because neural networks are inherently stochastic, it can be useful to train multiple networks with the same hyper parameters and take the average of their outputs as the model's prediction, to smooth output.`train_episodes`

:`int`

of the number of training episodes/epochs. A short discussion of the topic can be found here.`batch_size`

:`int`

of the number of observations per batch. Discussed here`decay`

:`float`

of the rate of decay of the learning rate. Also discussed here. Set to`0`

for no decay.`n_hidden`

:`int`

of the number of hidden states in the LSTM network. Discussed here.`n_layers`

:`int`

of the number of LSTM layers to include in the network. Also discussed here.`dropout`

:`float`

of the proportion of layers to drop in between LSTM layers. Discussed here.`criterion`

:`PyTorch loss function`

. Discussed here, list of available options in PyTorch here.`optimizer`

:`PyTorch optimizer`

. Discussed here, list of available options in PyTorch here. E.g.`torch.optim.SGD`

.`optimizer_parameters`

:`dictionary`

. Parameters for a particular optimizer, including learning rate. Information here. For instance, to change learning rate (default 1e-2), pass`{"lr":1e-2}`

, or weight_decay for L2 regularization, pass`{"lr":1e-2, "weight_decay":1e-3}`

. Learning rate discussed here.

## LSTM outputs

Assuming a model has been instantiated and trained with `model = LSTM(...)`

:

`model.train()`

: trains the network. Set`quiet=True`

to suppress printing of losses per epoch during training.`model.X`

: transformed data in the format the model was/will actually be trained on. A`numpy array`

of dimensions`n observations x n timesteps x n features`

.`model.y`

: one-dimensional list target values the model was/will be trained on.`model.predict(model.data)`

: given a dataframe with the same columns the model was trained on, returns a dataframe with date, actuals, and predictions, pass`model.data`

for performance on the training set.`model.predict(new_data)`

: generate dataframe of predictions on a new dataset. Generally should be the same dataframe as the training set, plus additional dates/datapoints.`model.mv_lstm`

: a`list`

of length`n_models`

containing the PyTorch networks.`model.train_loss`

: a`list`

of length`n_models`

containing the training losses of each of the trained networks.`model.ragged_preds(pub_lags, lag, new_data, start_date, end_date)`

: adds artificial missing data then returns a dataframe with date, actuals, and predictions. This is especially useful as a testing mechanism, to generate datasets to see how a trained model would have performed at different synthetic vintages or periods of time in the past.`pub_lags`

should be a list of`ints`

(in the same order as the columns of the original data) of length`n_features`

(i.e. excluding the target variable) dictating the normal publication lag of each of the variables.`lag`

is an int of how many periods back we want to simulate being, interpretable as last period relative to target period. E.g. if we are nowcasting June,`lag = -1`

will simulate being in May, where May data is published for variables with a publication lag of 0. It will fill with missings values that wouldn't have been available yet according to the publication lag of the variable + the`lag`

parameter. It will fill missings with the same method specified in the`fill_ragged_edges_func`

parameter in model instantiation.`model.gen_news(target_period, old_data, new_data)`

: Generates news between one data release to another, adding an element of causal inference to the network. Works by holding out new data column by column, recording differences between this prediction and the prediction on full data, and registering this difference as the new data's contribution to the prediction. Contributions are then scaled to equal the actual observed difference in prediction in the aggregate between the old dataset and the new dataset.`model.feature_contribution()`

: Generates a dataframe showing the relative feature importance of variables in the model using the permutation feature contribution method via RMSE on the train set.

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