Help for package arimasel

Title:

Cartesian Product-Based ARIMA Model Identification and Selection

Version:

0.2.0

Description:

Provides an alternative algorithm for ARIMA and seasonal ARIMA model identification based on Cartesian products of user-supplied parameter sets. Rather than relying on ACF/PACF plots or stepwise search (as in auto.arima()), the package exhaustively evaluates every candidate (p,d,q)(P,D,Q)[m] combination in the requested index sets, ranks all converged models by AIC, AICc, BIC, and HQIC simultaneously, computes Akaike weights for model uncertainty quantification, supports exogenous regressors, produces ensemble forecasts, evaluates candidate models by rolling-origin (expanding window) cross-validation, and provides publication-quality diagnostic and comparison plots. A feature-based exploratory data analysis suite computes scale-free time series characteristics (trend and seasonal strength, spectral entropy, autocorrelation, lumpiness, stability) in the spirit of Hyndman, Wang and Laptev (2015), and a feature-guided automatic search narrows the Cartesian product model space before the exhaustive search runs. The algorithm is flexible, transparent, and widely applicable for quick, reproducible ARIMA model selection in both academic research and industry forecasting pipelines. Applications are demonstrated with Nigerian macroeconomic time series data.

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

Depends:

R (≥ 4.0.0)

Imports:

stats, graphics, grDevices, utils, parallel

Suggests:

tseries, forecast, testthat (≥ 3.0.0), knitr, rmarkdown

VignetteBuilder:

knitr

RoxygenNote:

7.3.1

URL:

https://github.com/Olawaleawe/arimasel

BugReports:

https://github.com/Olawaleawe/arimasel/issues

NeedsCompilation:

Packaged:

2026-09-09 12:59:40 UTC; root

Author:

Olushina Olawale Awe

[aut, cre]

Maintainer:

Olushina Olawale Awe <olawaleawe@gmail.com>

Repository:

CRAN

Date/Publication:

2026-09-17 12:00:02 UTC

arimasel: Cartesian Product-Based ARIMA Model Identification and Selection

Description

Modelling and forecasting of time series data are essential components of data science and big data analytics. The Box-Jenkins methodology has gained tremendous popularity for modelling univariate time series, yet ACF/PACF plots often provide conflicting and biased pictures, making proper ARIMA model identification difficult.

arimasel proposes an alternative algorithm based on the mathematical principles of Cartesian products of sets. Given user-supplied index sets P, D, and Q (optionally combined with seasonal sets Ps, Ds, Qs at period m), the algorithm exhaustively fits every candidate (p,d,q)(P,D,Q)[m] combination, ranks all converged models by four information criteria simultaneously (AIC, AICc, BIC, HQIC), and quantifies model uncertainty via Akaike weights. The package additionally supports exogenous regressors, rolling-origin cross-validation for genuine out-of-sample evaluation (arima_cv), STL-based seasonal-strength diagnostics (seasonal_strength, suggest_D), feature-based exploratory data analysis (ts_eda, ts_features), and a feature-guided automatic search (smart_arima) that narrows the Cartesian product model space using time series characteristics before the exhaustive search runs. The algorithm is flexible, modular, and widely applicable – competing with and complementing stepwise approaches such as auto.arima().

Author(s)

Maintainer: Olushina Olawale Awe olawaleawe@gmail.com (ORCID)

Rolling-Origin Cross-Validation for a Cartesian Product ARIMA Result

Description

Evaluates the genuine out-of-sample forecasting accuracy of the model order selected by cart_arima using rolling-origin (expanding window) cross-validation – the time-series analogue of k-fold cross-validation, sometimes called "backtesting" in industry forecasting practice. Starting from an initial training window, the model is re-fitted with the same (p,d,q) (and seasonal, and xreg, if used) order at each origin, an h-step-ahead forecast is produced, and the forecast error is recorded. The window then expands by step observations and the process repeats to the end of the series. This complements in-sample information criteria (AIC/BIC/HQIC) with a direct, model-agnostic measure of forecasting performance – standard practice in modern applied and industrial time series work.

Usage

arima_cv(object, h = 1L, initial = NULL, step = 1L)

Arguments

object

An object of class "cartARIMA" (the model order, seasonal specification, and xreg of object$best_model are reused at every origin).

h

Positive integer forecast horizon evaluated at each origin. Default 1L.

initial

Integer; size of the first training window. Defaults to max(20L, floor(0.5 * n_obs)).

step

Integer; number of observations by which the training window expands between successive origins. Default 1L.

Value

An object of class "arimaCV" with components:

errors: A long-format data.frame with columns Origin, Horizon, Actual, Forecast, Error.
accuracy: A data.frame, one row per horizon, with RMSE, MAE, MAPE, and N (number of folds contributing to that horizon).
order: The (p,d,q) order reused at every origin.
seasonal: The seasonal order/period reused, or NULL.
n_folds: Number of rolling origins evaluated.
h, initial, step: As supplied.
call: The matched call.

Examples

set.seed(123)
x <- arima.sim(list(ar = 0.6), n = 120)
res <- cart_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)
cv <- arima_cv(res, h = 1, initial = 80)
print(cv)

Residual Diagnostics for a Cartesian Product ARIMA Result

Description

Produces a six-panel residual diagnostic plot for the best ARIMA model identified by cart_arima, and returns an object of class "arimaDiagnose" (with its own print method reporting the Shapiro-Wilk and Ljung-Box test results) for further inspection. The panels are:

Residuals over time.
Sample ACF of residuals.
Sample PACF of residuals.
Histogram of residuals with fitted Normal density.
Normal Q-Q plot.
Ljung-Box test p-values for lags 1 to lags.

Usage

arima_diagnose(object, lags = NULL, ...)

Arguments

object

An object of class "cartARIMA".

lags

Positive integer; maximum lag for the Ljung-Box plot. Default: min(20L, floor(object$n_obs / 5)).

...

Additional graphical parameters passed to base plot().

Value

An object of class "arimaDiagnose" with components ljung_box (a data.frame) and shapiro_wilk (the result of shapiro.test()), printed by its own print method.

Examples

set.seed(3)
x <- arima.sim(list(ar = 0.5), n = 80)
res <- cart_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)
arima_diagnose(res, lags = 15)

Forecast from a Cartesian Product ARIMA Selection Result

Description

Produces point forecasts and prediction intervals from a fitted "cartARIMA" object, either from the single best model or as an Akaike-weight-averaged ensemble across the top top_k models.

Usage

arima_forecast(
  object,
  h = 10L,
  newxreg = NULL,
  ensemble = FALSE,
  top_k = NULL,
  level = c(80, 95),
  plot = TRUE,
  ...
)

Arguments

object

An object of class "cartARIMA".

h

Positive integer; forecast horizon. Default: 10L.

newxreg

Optional matrix of future external regressors with h rows, required when the model in object was fitted with xreg.

ensemble

Logical; if TRUE, compute an Akaike-weighted ensemble forecast overlaid on the best-model forecast. Default: FALSE.

top_k

Integer; number of top models to include in the ensemble. Default: min(5L, object$n_converged).

level

Numeric vector of confidence levels for prediction intervals (values in (0,100)). Default: c(80, 95).

plot

Logical; if TRUE (default), produce a forecast plot.

...

Additional graphical arguments passed to plot().

Details

The ensemble point forecast is the weighted mean

\hat{y}^{\text{ens}}_t = \sum_{i=1}^{K} \tilde{w}_i \, \hat{y}^{(i)}_t,

where \tilde{w}_i are the re-normalised Akaike weights over the top K models and \hat{y}^{(i)}_t is the point forecast from model i. Prediction intervals are taken from the best model.

Value

A list (invisibly) with components:

mean: Numeric vector of best-model point forecasts.
lower: Matrix of lower PI bounds (nrow = h, ncol = length(level)).
upper: Matrix of upper PI bounds.
ensemble_mean: Numeric vector of ensemble forecasts (or NULL if ensemble = FALSE).
level: The confidence levels used.
model: The best-model string.
top_k: Number of ensemble members.

Examples

set.seed(7)
x <- arima.sim(list(ar = 0.6), n = 80)
res <- cart_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)
arima_forecast(res, h = 8, ensemble = TRUE, top_k = 3)

Format and Re-rank the ARIMA Model Comparison Table

Description

Extracts, optionally re-ranks, and truncates the model comparison table stored inside a "cartARIMA" object.

Usage

arima_table(object, criterion = NULL, top_n = NULL)

Arguments

object

An object of class "cartARIMA".

criterion

Character; criterion to rank by. One of "AIC", "AICc", "BIC", "HQIC". If NULL (default), the criterion used when cart_arima() was called is retained.

top_n

Integer; number of rows to return. If NULL, all converged models are returned.

Value

A data.frame with columns Model, p, d, q, (P, D, Q if a seasonal search was used), LogLik, AIC, AICc, BIC, HQIC, Rank, Delta, and Weight.

Examples

set.seed(1)
x <- arima.sim(list(ar = 0.5), n = 80)
res <- cart_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)
arima_table(res, criterion = "BIC", top_n = 5)

Akaike Weights and Evidence Ratios

Description

Given a numeric vector of information criterion values (lower is better), computes Akaike weights w_i = \exp(-\Delta_i/2) / \sum_j \exp(-\Delta_j/2) and evidence ratios ER_i = w_{\text{best}} / w_i relative to the best (lowest-IC) model.

Usage

arima_weights(criteria_values, names_vec = NULL)

Arguments

criteria_values

A numeric vector of IC values, length >= 2.

names_vec

Optional character vector of model names; if NULL, names(criteria_values) or "Model_i" labels are used.

Value

A data.frame with columns Model, IC_value, Delta, Weight, and EvidenceRatio, sorted by ascending Delta.

Examples

ic_vals <- c(ARIMA_110 = 200.1, ARIMA_011 = 198.4, ARIMA_210 = 201.7)
arima_weights(ic_vals)

Cartesian Product (Seasonal) ARIMA Model Identification and Selection

Description

The flagship function of arimasel. Given sets P, D, and Q of non-negative integers (and, optionally, seasonal sets P_s, D_s, Q_s at period m), the algorithm:

Computes the Cartesian product P \times D \times Q (optionally combined with P_s \times D_s \times Q_s).
Fits every candidate (S)ARIMA model, exhaustively rather than stepwise, optionally in parallel.
Ranks all converged models by AIC, AICc, BIC, and HQIC.
Computes Akaike weights and a criterion-vote table.
Returns the best model object and a full comparison table.

Usage

cart_arima(
  x,
  p_set = 0:2,
  d_set = 0:1,
  q_set = 0:2,
  seasonal = NULL,
  xreg = NULL,
  criterion = c("AIC", "AICc", "BIC", "HQIC"),
  top_n = 10L,
  parallel = FALSE,
  n_cores = NULL,
  ...
)

Arguments

x

A numeric vector or a ts object representing the time series. Must have at least 10 observations.

p_set

Integer vector of AR orders p \ge 0. Default: 0:2.

d_set

Integer vector of differencing orders d \ge 0. Default: 0:1.

q_set

Integer vector of MA orders q \ge 0. Default: 0:2.

seasonal

Optional named list describing a seasonal search, with elements P, D, Q (integer index sets, each defaulting to 0:1) and period (the seasonal period m; required). When supplied, every combination of (p,d,q) and (P,D,Q)_m is fitted as a seasonal ARIMA model. If NULL (default), a non-seasonal search is performed.

xreg

Optional numeric vector or matrix of external regressors, with number of rows/length equal to length(x), passed to every candidate model fit (regression with ARIMA errors).

criterion

Primary ranking criterion: one of "AIC" (default), "AICc", "BIC", or "HQIC".

top_n

Integer; maximum number of models to include in the abbreviated comparison table (accessible via obj$table). Default: 10L. The full table is always stored in obj$full_table.

parallel

Logical; if TRUE, candidate models are fitted in parallel using mclapply (ignored, with a serial fallback, on Windows where forking is unavailable). Default FALSE.

n_cores

Integer number of worker processes to use when parallel = TRUE. Defaults to max(1L, parallel::detectCores() - 1L).

...

Additional arguments passed to arima, e.g. method = "ML", include.mean = FALSE.

Value

An object of class "cartARIMA" with components:

best_model: The fitted Arima object for the top-ranked model.
best_model_str: Character string, e.g. "ARIMA(1,1,1)".
criterion: The primary ranking criterion.
table: A data.frame of the top top_n models with LogLik, AIC, AICc, BIC, HQIC, Delta, Weight, Rank.
full_table: The complete ranked table (all converged models).
vote_table: A data.frame showing how many criteria each model wins.
failed_models: Character vector of ARIMA strings that failed to converge.
n_total: Total number of candidate models attempted.
n_converged: Number of models that converged successfully.
p_set, d_set, q_set: The index sets used.
seasonal: The validated seasonal specification, or NULL.
xreg: The external regressors used, or NULL.
data: The original time series (as a ts object).
n_obs: Length of the original series.
call: The matched call.

Examples

set.seed(42)
x <- arima.sim(list(ar = 0.7, ma = -0.3), n = 100)
result <- cart_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)
print(result)


## Seasonal search on monthly data
data(inflation_ng)
res_s <- cart_arima(inflation_ng, p_set = 0:1, d_set = 0:1, q_set = 0:1,
                    seasonal = list(P = 0:1, D = 0:1, Q = 0:1, period = 12))
print(res_s)

Compare cart_arima with auto.arima()

Description

Fits the Cartesian product model and, if the forecast package is available, compares it with auto.arima() on in-sample criteria and optionally on a hold-out test set. Returns an object of class "compareArima" with its own print method.

Usage

compare_arima(
  x,
  p_set = 0:2,
  d_set = 0:1,
  q_set = 0:2,
  seasonal = NULL,
  criterion = "AIC",
  holdout = 0L,
  ...
)

Arguments

x

A numeric vector or ts object.

p_set, d_set, q_set

Index sets for cart_arima.

seasonal

Optional seasonal specification passed to cart_arima (see its seasonal argument). When supplied, auto.arima() is also fitted with seasonal = TRUE for a like-for-like comparison.

criterion

Primary criterion for cart_arima. Default: "AIC".

holdout

Integer; number of observations to reserve as a test set for out-of-sample evaluation. 0L (default) disables holdout.

...

Additional arguments passed to cart_arima.

Value

An object of class "compareArima", a list with components cart_arima_result, comparison_table, and (if forecast is available) auto_arima_model and winner, printed by its own print method.

Examples

set.seed(11)
x <- arima.sim(list(ar = 0.6), n = 80)
compare_arima(x, p_set = 0:2, d_set = 0:1, q_set = 0:2)

Cartesian Product of ARIMA (or Seasonal ARIMA) Parameter Sets

Description

Displays and returns the Cartesian product P \times D \times Q (optionally combined with a seasonal product P_s \times D_s \times Q_s) of user-supplied non-negative integer sets, enumerating all candidate ARIMA(p,d,q) or seasonal ARIMA(p,d,q)(P,D,Q)_m models. This is the first step of the arimasel algorithm.

Usage

cp_sets(p_set = 0:2, d_set = 0:1, q_set = 0:2, seasonal = NULL)

Arguments

p_set

Integer vector of autoregressive orders p \ge 0. Default: 0:2.

d_set

Integer vector of differencing orders d \ge 0. Default: 0:1.

q_set

Integer vector of moving-average orders q \ge 0. Default: 0:2.

seasonal

Optional named list with integer elements P, D, Q (seasonal index sets, each defaulting to 0:1) and period (the seasonal period m, required). When supplied, the seasonal Cartesian product is combined with P \times D \times Q.

Value

An object of class "cartProduct" with components p_set, d_set, q_set, seasonal, product (a data.frame), n_models, and model_strings, printed by its own print method.

Examples

cp_sets(0:1, 0:1, 0:1)
cp_sets(p_set = c(0,1,2), d_set = 1, q_set = c(0,1))
cp_sets(0:1, 0:1, 0:1, seasonal = list(P = 0:1, D = 0:1, Q = 0:1, period = 12))

Monthly USD/NGN Exchange Rate – Nigeria, 2010-2023

Description

A univariate monthly time series of the US dollar to Nigerian Naira (NGN) exchange rate from January 2010 to December 2023. The series incorporates structural breaks reflecting major exchange-rate policy changes in Nigeria, including the 2016 devaluation and the 2023 unification of exchange-rate windows.

Usage

exchange_ng

Format

A ts object of length 168 with frequency = 12, starting in January 2010.

Source

Simulated to reflect documented CBN/FMDQ exchange-rate regimes. See vignette("arimasel-intro").

Examples

data(exchange_ng)
plot(exchange_ng, main = "USD/NGN Exchange Rate", ylab = "NGN per USD")

Annual GDP Growth Rate – Nigeria, 1990-2023

Description

A univariate annual time series of Nigeria's GDP growth rate (percentage) from 1990 to 2023, based on publicly available World Bank and IMF data patterns. Suitable for demonstrating ARIMA modelling on short annual series.

Usage

gdp_ng

Format

A ts object of length 34 with frequency = 1, starting in 1990.

Source

Simulated to reflect documented Nigerian GDP growth patterns (World Bank WDI, IMF WEO). See vignette("arimasel-intro").

Examples

data(gdp_ng)
plot(gdp_ng, main = "Nigeria Annual GDP Growth Rate (%)", ylab = "%", xlab = "Year")
abline(h = 0, lty = 2)

Hannan-Quinn Information Criterion

Description

Computes the Hannan-Quinn Information Criterion (HQIC) for a fitted ARIMA model object. HQIC is defined as

\mathrm{HQIC} = -2\hat{\ell} + 2k\ln(\ln n),

where \hat{\ell} is the maximised log-likelihood, k is the total number of free parameters (coefficients plus \sigma^2), and n is the number of observations used in fitting.

Usage

hqic(object, k = 2)

Arguments

object

A fitted model of class "Arima" (from arima).

k

Numeric penalty multiplier; default 2.

Value

A single numeric value.

References

Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B, 41(2), 190–195.

Examples

x <- cumsum(rnorm(80))
fit <- arima(x, order = c(1, 1, 0))
hqic(fit)

Monthly CPI Inflation Rate – Nigeria, 2000-2023

Description

A univariate monthly time series of Nigeria's consumer price index (CPI) year-on-year inflation rate (percentage) from January 2000 to December 2023, simulated to reflect documented NBS/CBN inflationary regimes including low-inflation (2000-2014), the commodity-shock era (2015-2017), and the post-COVID acceleration (2020-2023).

Usage

inflation_ng

Format

A ts object of length 288 with frequency = 12, starting in January 2000.

Source

Simulated to reflect documented Nigerian CPI data patterns (NBS, CBN Annual Reports). See vignette("arimasel-intro").

Examples

data(inflation_ng)
plot(inflation_ng, main = "Nigeria Monthly CPI Inflation (%)", ylab = "%")

Plot Method for arimaCV Objects

Description

Plot Method for arimaCV Objects

Usage

## S3 method for class 'arimaCV'
plot(x, type = c("rmse", "forecasts"), ...)

Arguments

x

An object of class "arimaCV".

type

Character; "rmse" (default) plots RMSE/MAE by horizon; "forecasts" overlays every rolling-origin forecast against the actual series (horizon 1 only).

...

Additional graphical parameters passed to base plot functions.

Value

Invisibly returns x.

Plot Method for cartARIMA Objects

Description

Produces one of several publication-quality diagnostic plots for a fitted "cartARIMA" object.

Usage

## S3 method for class 'cartARIMA'
plot(
  x,
  type = c("criteria", "weights", "surface", "fitted", "seasonal"),
  criterion = NULL,
  top_n = 10L,
  ...
)

Arguments

x

An object of class "cartARIMA".

type

Character; plot type. One of:

"criteria": Horizontal bar chart of IC values for top models.
"weights": Bar chart of Akaike model weights.
"surface": Criterion heat map over the p \times q grid (for the most frequently occurring d value in the top models).
"fitted": Time series overlay: observed vs. fitted values.
"seasonal": STL decomposition of the original series (trend, seasonal, remainder); requires frequency(x$data) > 1.

criterion

Character; criterion to display. Defaults to the one used in cart_arima().

top_n

Integer; number of models to include in "criteria" and "weights" plots. Default: 10.

...

Additional graphical parameters passed to base plot functions.

Value

Invisibly returns x.

Print Method for arimaCV Objects

Description

Print Method for arimaCV Objects

Usage

## S3 method for class 'arimaCV'
print(x, ...)

Arguments

x

An object of class "arimaCV".

...

Currently unused.

Value

Invisibly returns x.

Print Method for arimaDiagnose Objects

Description

Print Method for arimaDiagnose Objects

Usage

## S3 method for class 'arimaDiagnose'
print(x, ...)

Arguments

x

An object of class "arimaDiagnose".

...

Currently unused.

Value

Invisibly returns x.

Print Method and Accessors for cartARIMA Objects

Description

print and accessor methods (coef, residuals, fitted, AIC, BIC, logLik) for objects of class "cartARIMA", all of which delegate to object$best_model.

Usage

## S3 method for class 'cartARIMA'
print(x, ...)

## S3 method for class 'cartARIMA'
coef(object, ...)

## S3 method for class 'cartARIMA'
residuals(object, ...)

## S3 method for class 'cartARIMA'
fitted(object, ...)

## S3 method for class 'cartARIMA'
AIC(object, ..., k = 2)

## S3 method for class 'cartARIMA'
BIC(object, ...)

## S3 method for class 'cartARIMA'
logLik(object, ...)

Arguments

x, object

An object of class "cartARIMA".

...

Currently unused (accessors pass ... through to the corresponding method on object$best_model where applicable).

k

Numeric AIC penalty multiplier (see AIC); default 2.

Value

Invisibly returns x for print; the accessors return the corresponding value from object$best_model.

Print Method for compareArima Objects

Description

Print Method for compareArima Objects

Usage

## S3 method for class 'compareArima'
print(x, ...)

Arguments

x

An object of class "compareArima".

...

Currently unused.

Value

Invisibly returns x.

Print Method for stationarityTest Objects

Description

Print Method for stationarityTest Objects

Usage

## S3 method for class 'stationarityTest'
print(x, ...)

Arguments

x

An object of class "stationarityTest".

...

Currently unused.

Value

Invisibly returns x.

Print Method for tsEda Objects

Description

Print Method for tsEda Objects

Usage

## S3 method for class 'tsEda'
print(x, ...)

Arguments

x

An object of class "tsEda".

...

Currently unused.

Value

Invisibly returns x.

Trend and Seasonal Strength via STL Decomposition

Description

Computes the trend and seasonal strength measures of Wang, Smith and Hyndman (2006) from an STL decomposition (stl):

F_S = \max\left(0, 1 - \frac{\mathrm{Var}(R_t)}{\mathrm{Var}(S_t + R_t)}\right)

for seasonal strength, and analogously for trend strength using T_t + R_t. Values close to 1 indicate a strong, well-defined trend or seasonal pattern; values close to 0 indicate little or none. These are modern, model-free diagnostics that complement formal unit-root tests when deciding whether to include seasonal terms in a model search.

Usage

seasonal_strength(x, period = NULL, s.window = "periodic")

Arguments

x

A numeric vector or ts object with frequency > 1.

period

Optional integer seasonal period, used when x is not already a ts object with a known frequency.

s.window

Passed to stl; default "periodic".

Value

A list with components trend_strength, seasonal_strength, period, and stl (the underlying stl decomposition object).

References

Wang, X., Smith, K. A. and Hyndman, R. J. (2006). Characteristic-based clustering for time series data. Data Mining and Knowledge Discovery, 13(3), 335–364.

Examples

data(inflation_ng)
seasonal_strength(inflation_ng)

Feature-Guided Automatic (Seasonal) ARIMA Search

Description

A "smart" wrapper around cart_arima that first runs feature-based exploratory analysis (ts_features, suggest_d, suggest_D) to narrow the search space automatically, then performs the usual exhaustive Cartesian-product search within that narrowed space. This mirrors modern automatic forecasting pipelines that use time series features to steer model selection (Hyndman, Wang and Laptev, 2015; Talagala, Hyndman and Athanasopoulos, 2023) while retaining full transparency: every decision the function makes is printed, and the underlying cart_arima call is always available for a fully manual search.

Usage

smart_arima(
  x,
  p_set = 0:3,
  q_set = 0:3,
  P_set = 0:1,
  Q_set = 0:1,
  period = NULL,
  criterion = "AIC",
  top_n = 10L,
  parallel = FALSE,
  n_cores = NULL,
  ...
)

Arguments

x

A numeric vector or ts object.

p_set, q_set

Non-seasonal AR/MA index sets to search (the differencing order d_set is chosen automatically). Defaults 0:3 and 0:3.

P_set, Q_set

Seasonal AR/MA index sets, used only when a seasonal search is triggered. Defaults 0:1 and 0:1.

period

Optional integer seasonal period, used when x is not already a seasonal ts object. If NULL and x has no usable frequency, the search is non-seasonal.

criterion, top_n, parallel, n_cores, ...

Passed through to cart_arima.

Details

Specifically: the differencing order d is restricted to suggest_d(x) (plus one higher order as a safety margin), and, when x has a seasonal frequency greater than 1 (or period is supplied), a seasonal search is automatically enabled with D restricted to suggest_D(x).

Value

An object of class "cartARIMA", identical in structure to the return value of cart_arima, with an additional eda component holding the ts_features output used to guide the search.

References

Hyndman, R. J., Wang, E. and Laptev, N. (2015). Large-scale unusual time series detection. 2015 IEEE International Conference on Data Mining Workshop, 1616–1619.

Talagala, T. S., Hyndman, R. J. and Athanasopoulos, G. (2023). Meta-learning how to forecast time series. Journal of Forecasting, 42(6), 1476–1501.

Examples

data(gdp_ng)
res <- smart_arima(gdp_ng, p_set = 0:1, q_set = 0:1)
print(res)


## Seasonal monthly series: seasonal search is enabled automatically
data(inflation_ng)
res_seas <- smart_arima(inflation_ng, p_set = 0:1, q_set = 0:1)
print(res_seas)

Battery of Stationarity Tests

Description

Runs the Augmented Dickey-Fuller (ADF) test on the supplied time series. If the tseries package is installed, the Phillips-Perron (PP) and KPSS tests are also performed. Returns an object of class "stationarityTest" (a data.frame of test statistics, approximate p-values, and per-test conclusions, plus a consensus conclusion) with its own print method.

Usage

stationarity_test(x, lags = NULL, alpha = 0.05)

Arguments

x

A numeric vector or ts object.

lags

Integer; ADF lag order. If NULL (default), chosen as \lfloor (n-1)^{1/3} \rfloor.

alpha

Significance level for the consensus decision. Default: 0.05.

Value

An object of class "stationarityTest", printed by its own print method. Underlying columns Test, Statistic, p_value, and Conclusion, plus attributes consensus and suggested_d.

Examples

set.seed(5)
x <- cumsum(rnorm(80))
stationarity_test(x)

Recommend a Seasonal Differencing Order

Description

Recommends a seasonal differencing order D \in \{0, 1\} using the seasonal-strength heuristic of Wang, Smith and Hyndman (2006) via seasonal_strength: a seasonal difference is recommended when the seasonal strength F_S exceeds threshold (default 0.64, the rule used in forecast::nsdiffs(test = "seas")).

Usage

suggest_D(x, period = NULL, threshold = 0.64, verbose = FALSE)

Arguments

x

A numeric vector or ts object.

period

Optional integer seasonal period (required if x is not already a seasonal ts object).

threshold

Seasonal-strength threshold above which a seasonal difference is recommended. Default 0.64.

verbose

Logical; if TRUE, print the seasonal strength. Default FALSE.

Value

A single integer, 0L or 1L.

References

Wang, X., Smith, K. A. and Hyndman, R. J. (2006). Characteristic-based clustering for time series data. Data Mining and Knowledge Discovery, 13(3), 335–364.

Examples

data(inflation_ng)
suggest_D(inflation_ng)

Recommend a Differencing Order

Description

Applies the ADF test battery via stationarity_test and returns the recommended integer differencing order d \in \{0, 1, 2\}. Differencing is applied iteratively until stationarity is detected or the maximum d is reached.

Usage

suggest_d(x, max_d = 2L, alpha = 0.05, verbose = FALSE)

Arguments

x

A numeric vector or ts object.

max_d

Maximum differencing order to consider. Default: 2L.

alpha

Significance level. Default: 0.05.

verbose

Logical; if TRUE, print test summaries. Default: FALSE.

Value

A single non-negative integer.

Examples

set.seed(9)
x <- cumsum(rnorm(80))
suggest_d(x)

Summary Method for arimaCV Objects

Description

Summary Method for arimaCV Objects

Usage

## S3 method for class 'arimaCV'
summary(object, ...)

Arguments

object

An object of class "arimaCV".

...

Currently unused.

Value

Invisibly returns object.

Summary Method for cartARIMA Objects

Description

Summary Method for cartARIMA Objects

Usage

## S3 method for class 'cartARIMA'
summary(object, ...)

Arguments

object

An object of class "cartARIMA".

...

Currently unused.

Value

Invisibly returns object.

Exploratory Data Analysis for a Time Series

Description

Produces a console summary and a multi-panel exploratory plot for a univariate time series before model identification: the time plot, distribution, autocorrelation structure, and (if applicable) seasonal pattern. Intended as the first step of the arimasel workflow, complementing formal stationarity testing (stationarity_test) and feature extraction (ts_features).

Usage

ts_eda(x, period = NULL, lag.max = NULL, ...)

Arguments

x

A numeric vector or ts object.

period

Optional integer seasonal period, used when x is not already a seasonal ts object.

lag.max

Maximum lag shown in the ACF/PACF panels. Default min(24L, floor(length(x) / 4)).

...

Additional graphical parameters passed to the time plot.

Value

An object of class "tsEda" with components features (the output of ts_features), stationarity (the output of stationarity_test), and suggested_d /suggested_D (recommended differencing orders), printed by its own print method.

Examples

data(inflation_ng)
eda <- ts_eda(inflation_ng)
eda$features

Feature-Based Time Series Summary

Description

Computes a compact vector of numeric characteristics of a time series in the spirit of feature-based time series analysis (Hyndman, Wang and Laptev, 2015): a scale-free description of a series' trend, seasonality, autocorrelation, entropy, and stability that can be used to compare many series, cluster them, or guide automatic model search (see smart_arima).

Usage

ts_features(x, period = NULL)

Arguments

x

A numeric vector or ts object.

period

Optional integer seasonal period, used when x is not already a seasonal ts object and trend/seasonal strength are requested. If omitted and x has no usable frequency, seasonal features are returned as NA.

Value

A one-row data.frame with columns:

n: Series length.
mean, sd: Sample mean and standard deviation.
skewness, kurtosis: Standardised third and fourth moments (excess kurtosis).
trend_strength, seasonal_strength: From seasonal_strength; NA if no seasonal period is available.
entropy: Spectral entropy in [0, 1]; values near 0 indicate a strongly predictable (structured) series, values near 1 indicate near white noise.
acf1: First-lag autocorrelation of x.
lumpiness, stability: Variance of the variances / means across ten equal-sized blocks of the series – large values flag heteroscedasticity or level shifts.
adf_stat, adf_pvalue: Augmented Dickey-Fuller test statistic and approximate p-value (see stationarity_test).

References

Hyndman, R. J., Wang, E. and Laptev, N. (2015). Large-scale unusual time series detection. 2015 IEEE International Conference on Data Mining Workshop, 1616–1619.

Examples

data(gdp_ng)
ts_features(gdp_ng)

Package {arimasel}

arimasel: Cartesian Product-Based ARIMA Model Identification and Selection

Description

Author(s)

See Also

Rolling-Origin Cross-Validation for a Cartesian Product ARIMA Result

Description

Usage

Arguments

Value

See Also

Examples

Residual Diagnostics for a Cartesian Product ARIMA Result

Description

Usage

Arguments

Value

Examples

Forecast from a Cartesian Product ARIMA Selection Result

Description

Usage

Arguments

Details

Value

Examples

Format and Re-rank the ARIMA Model Comparison Table

Description

Usage

Arguments

Value

Examples

Akaike Weights and Evidence Ratios

Description

Usage

Arguments

Value

Examples

Cartesian Product (Seasonal) ARIMA Model Identification and Selection

Description

Usage

Arguments

Value

See Also

Examples

Compare cart_arima with auto.arima()

Description

Usage

Arguments

Value

Examples

Cartesian Product of ARIMA (or Seasonal ARIMA) Parameter Sets

Description

Usage

Arguments

Value

Examples

Monthly USD/NGN Exchange Rate – Nigeria, 2010-2023

Description

Usage

Format

Source

Examples

Annual GDP Growth Rate – Nigeria, 1990-2023

Description

Usage

Format

Source

Examples

Hannan-Quinn Information Criterion

Description

Usage

Arguments

Value

References

Examples

Monthly CPI Inflation Rate – Nigeria, 2000-2023

Description

Usage

Format

Source