Transfer Function and ARIMA Models.

tfarima

Overview

tfarima provides a comprehensive framework for building customized Transfer Function and ARIMA models with multiple operators and parameter restrictions. The package implements exact maximum likelihood estimation and offers a wide range of tools for time series analysis.

Key Features

• Flexible model specification: Build ARIMA and transfer function models with multiple lag polynomials and parameter restrictions
• Model identification: Tools for identifying appropriate model structures
• Estimation methods: Exact or conditional maximum likelihood estimation
• Diagnostic checking: Comprehensive model validation tools
• Automatic outlier detection: Identify and handle outliers in time series
• Calendar effects: Model trading day, Easter, and leap year effects
• Forecasting: Generate predictions with confidence intervals
• Seasonal adjustment: Decompose time series into trend, seasonal, and irregular components

Installation

Install the stable version from CRAN:

install.packages("tfarima")

Or install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("gallegoj/tfarima")

Quick Start

library(tfarima)

# Load example data
data(rsales)

# Build a basic ARIMA model with seasonal components
model <- um(rsales, 
            i = list(1, c(1, 12)),        # Regular and seasonal differences
            ma = list(1, c(1, 12)),       # MA(1) and seasonal MA(1)
            bc = TRUE)                     # Box-Cox transformation

# Fit the model
fitted_model <- fit(model)

# Display results
summary(fitted_model)

# Generate forecasts
predictions <- predict(fitted_model, n.ahead = 12)
plot(predictions)

# Diagnostic checking
tsdiag(fitted_model)

Main Functions

Model Building

• um(): Build univariate ARIMA models
• tfm(): Build transfer function models
• lagpol(): Create lag polynomials with parameter restrictions

Model Estimation and Selection

• fit(): Estimate model parameters using exact or conditional ML
• outliers(): Detect and model outliers automatically
• calendar(): Add calendar effects (trading days, Easter, leap year)

Model Evaluation

• tsdiag(): Diagnostic checking plots
• residuals(): Extract model residuals
• AIC(), logLik(): Information criteria and likelihood

Forecasting and Decomposition

• predict(): Generate forecasts
• seasadj(): Seasonal adjustment
• ucomp(): Unobserved components decomposition

Example: Seasonal Adjustment

# Load retail sales data
data(rsales)

# Build and fit model with calendar effects
model <- um(rsales, 
            i = list(1, c(1, 12)), 
            ma = list(1, c(1, 12)), 
            bc = TRUE)

# Add calendar effects
model_cal <- calendar(model, easter = TRUE)
fitted <- fit(model_cal)

# Perform seasonal adjustment
sa <- seasadj(fitted)

# Plot results
plot(sa)

Example: Transfer Function Model

# Load gas furnace data
data(seriesJ)

# Build transfer function model
model <- tfm(seriesJ$output, 
             inputs = list(seriesJ$input),
             orders = list(c(3, 2, 0)))

# Fit the model
fitted <- fit(model)

# Summary and diagnostics
summary(fitted)
tsdiag(fitted)

Documentation

For more detailed information and examples, see:

• Package vignette: vignette("tfarima")
• Function documentation: help(package = "tfarima")
• CRAN page: https://CRAN.R-project.org/package=tfarima

References

The package implements methods from:

• Box, G.E.P., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control. John Wiley & Sons.

• Box, G.E.P., Pierce, D.A. and Newbold, D.A. (1987). Estimating Trend and Growth Rates in Seasonal Time Series. Journal of the American Statistical Association, 82(397), 276-282.

• Bell, W.R. and Hillmer, S.C. (1983). Modeling Time Series with Calendar Variation. Journal of the American Statistical Association, 78(383), 526-534.

• Chen, C. and Liu, L.M. (1993). Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of the American Statistical Association, 88(421), 284-297.

License

GPL (>= 2)

Author

José L. Gallego

Issues and Contributions

To report bugs or request features, please visit: https://github.com/gallegoj/tfarima/issues.