Package 'SMOARIMA'

Accuracy Measures for SMO-ARIMA Model

Description

The accuracy_smo function computes forecast accuracy measures for a fitted SMO-ARIMA model using the observed values of the test series and the corresponding forecasts.

Usage

accuracy_smo(
  object,
  test
)

Arguments

object	An object of class "smoarima" returned by fit_smo().
test	A univariate test time series (ts) containing the observed values corresponding to the forecast horizon. For the internal holdout evaluation created by fit_smo(), use object$test.

Details

The accuracy_smo function compares the forecasts generated by the fitted SMO-ARIMA model with the observed test data and computes commonly used forecast accuracy measures. The function returns Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Scaled Error (MASE).

Value

MAE	Mean Absolute Error.
MAPE	Mean Absolute Percentage Error.
MSE	Mean Squared Error.
RMSE	Root Mean Square Error.
MASE	Mean Absolute Scaled Error.
AIC	Akaike information criterion of the fitted model.
BIC	Bayesian information criterion of the fitted model.

References

Hyndman, R. J. and Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688.

See Also

fit_smo, forecast_smo

Examples

data(AirPassengers)

fit <- fit_smo(
  AirPassengers,
  population = 4,
  groups = 2,
  max.iter = 2,
  p.max = 1,
  d.max = 1,
  q.max = 1,
  local.limit = 2,
  global.limit = 2
)

acc <- accuracy_smo(
  fit,
  fit$test
)

acc

---

Spider Monkey Optimization based ARIMA Model Fitting

Description

The fit_smo function automatically identifies the optimal ARIMA (p, d, q) model using the Spider Monkey Optimization (SMO) algorithm. The selected model is fitted to the input time series and returned as an object of class "smoarima".

Usage

fit_smo(
  data,
  population = 30,
  groups = 5,
  max.iter = 80,
  p.max = 3,
  d.max = 2,
  q.max = 3,
  alpha = 0.7,
  local.limit = 10,
  global.limit = 15,
  train.prop = 0.80,
  seed = 42
)

Arguments

data	Input univariate time series (ts) object.
population	Population size of the Spider Monkey Optimization algorithm. Default is 30.
groups	Number of spider monkey groups. Default is 5.
max.iter	Maximum number of optimization iterations. Default is 80.
p.max	Maximum autoregressive (AR) order. Default is 3.
d.max	Maximum differencing order. Default is 2.
q.max	Maximum moving average (MA) order. Default is 3.
alpha	Weight assigned to the normalized AIC in the objective function. The remaining weight (1-alpha) is assigned to the normalized RMSE. Default is 0.7.
local.limit	Maximum number of consecutive non-improving iterations allowed for a local leader before the corresponding group is reinitialized. Default is 10.
global.limit	Maximum number of consecutive non-improving iterations allowed for the global leader before group membership is reorganized. Default is 15.
train.prop	Proportion of observations assigned to the training sample used for model estimation during order selection. It must be strictly between 0 and 1. Default is 0.80.
seed	Random seed for reproducibility. Default is 42.

Details

The Spider Monkey Optimization (SMO) algorithm searches for the optimal ARIMA order (p,d,q) by minimizing a weighted objective function based on normalized Akaike Information Criterion (AIC) and Root Mean Square Error (RMSE).

Value

model	Fitted ARIMA model.
order	Selected ARIMA order (p,d,q).
coefficients	Estimated ARIMA coefficients.
fitted	Fitted values.
residuals	Model residuals.
AIC	Akaike Information Criterion.
BIC	Bayesian Information Criterion.
logLik	Log-likelihood of the fitted model.
runtime	Execution time (seconds).
convergence	Optimization convergence history.

References

Bansal, J. C., Sharma, H., Jadon, S. S. and Clerc, M. (2014). Spider Monkey Optimization Algorithm for Numerical Optimization. Memetic Computing, 6, 31–47.

Box, G. E. P., Jenkins, G. M., Reinsel, G. C. and Ljung, G. M. (2016). Time Series Analysis: Forecasting and Control. 5th Edition. Wiley.

See Also

accuracy_smo, forecast_smo

Examples

data(AirPassengers)

fit <- fit_smo(
  data = AirPassengers,
  population = 4,
  groups = 2,
  max.iter = 2,
  p.max = 1,
  d.max = 1,
  q.max = 1,
  local.limit = 2,
  global.limit = 2
)

fit$order

fit$AIC

---

Forecasting using Spider Monkey Optimized ARIMA Model

Description

The forecast_smo function generates forecasts from a fitted SMO-ARIMA model obtained using the fit_smo function. Point forecasts together with the corresponding prediction intervals are returned for the specified forecast horizon.

Usage

forecast_smo(
  object,
  h = 10,
  level = c(80, 95)
)

Arguments

object	An object of class "smoarima" returned by fit_smo().
h	Forecast horizon. Default is 10.
level	Confidence level(s) for prediction intervals. Default is c(80,95).

Details

The forecast_smo function generates forecasts from the fitted ARIMA model selected using the Spider Monkey Optimization (SMO) algorithm. Forecasts are produced for the specified forecast horizon, along with lower and upper prediction intervals corresponding to the requested confidence level(s).

Value

method	Forecasting method used.
model	Fitted SMO-ARIMA model.
mean	Point forecasts.
lower	Lower prediction limits.
upper	Upper prediction limits.
level	Confidence level(s) used for prediction intervals.

References

Hyndman, R. J. and Athanasopoulos, G. (2021). Forecasting: Principles and Practice. 3rd Edition. OTexts, Melbourne, Australia.

See Also

fit_smo, accuracy_smo

Examples

data(AirPassengers)

fit <- fit_smo(
  AirPassengers,
  population = 4,
  groups = 2,
  max.iter = 2,
  p.max = 1,
  d.max = 1,
  q.max = 1,
  local.limit = 2,
  global.limit = 2
)

fc <- forecast_smo(
  fit,
  h = 12,
  level = c(80, 95)
)

fc

plot(fc)

---