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Ivan Svetunkov edited this page Jan 30, 2026 · 10 revisions

Visualisation and Output Methods

This page documents the methods for visualising and printing smooth models. These methods work with objects returned by ADAM, ES, CES, SSARIMA, MSARIMA, GUM, SMA, and OES.

print()

Prints a concise summary of the model to the console.

R Usage

model <- adam(AirPassengers, "MMM", lags=12, h=12, holdout=TRUE)
print(model)
# Or simply:
model

Python Usage

model = ADAM(model="MMM", lags=12)
model.fit(AirPassengers)

print(model)

Output

The print method displays:

  • Model type (e.g., "ETS(M,M,M)")
  • Initialisation type
  • Distribution used
  • Loss function value
  • Estimated parameters (persistence, phi)
  • Number of parameters and observations
  • Information criteria (AIC, AICc, BIC, BICc)
  • If holdout=TRUE, the error measures for the holdout are also printed

Note: In Python, the error measures are not automatically calculated for the holdout set.

Example Output

Time elapsed: 2.73 seconds
Model estimated using adam() function: ETS(MMM)
With backcasting initialisation
Distribution assumed in the model: Gamma
Loss function type: likelihood; Loss function value: 473.813
Persistence vector g:
 alpha   beta  gamma 
0.6029 0.0001 0.2600 

Sample size: 132
Number of estimated parameters: 4
Number of degrees of freedom: 128
Information criteria:
     AIC     AICc      BIC     BICc 
955.6260 955.9410 967.1573 967.9262 

Forecast errors:
ME: -20.52; MAE: 20.729; RMSE: 26.218
sCE: -93.809%; Asymmetry: -97.1%; sMAE: 7.897%; sMSE: 0.998%
MASE: 0.861; RMSSE: 0.837; rMAE: 0.273; rRMSE: 0.255

plot()

Produces diagnostic plots for smooth models. Multiple plot types are available depending on the model.

Note: Not yet implemented in Python.

R Usage

# Basic diagnostic plots
model <- adam(AirPassengers, "ZZZ", lags=12, h=12, holdout=TRUE)

# Single plot
plot(model, which=1)

# Multiple plots
par(mfcol=c(3,4))
plot(model, which=c(1:11))
par(mfcol=c(1,1))

# Decomposition plot
plot(model, which=12)

Available Plots

which Plot Type Description
1 Actuals vs Fitted Time series plot of actual values and fitted values
2 Standardised residuals Residuals divided by their standard deviation
3 Histogram Distribution of standardised residuals
4 ACF Autocorrelation function of residuals
5 PACF Partial autocorrelation function of residuals
6 Q-Q plot Normal probability plot of residuals
7 Fitted vs Actuals (scatter) Scatterplot with fitted on x-axis
8 Squared residuals vs Fitted Heteroscedasticity diagnostic
9 ACF of squared residuals ARCH effects diagnostic
10 Residuals vs Time Time plot of residuals
11 Forecast fan chart Point forecasts with prediction intervals
12 Decomposition Components of the model (level, trend, seasonal)

Parameters

Parameter Type (R) Type (Python) Default Description
x adam/smooth - - Fitted model object
which integer vector - c(1,2,4,6) Which plots to produce
level numeric - 0.95 Confidence level for intervals
legend logical - FALSE Show legend on plots
ask logical - TRUE Prompt before each plot
lowess logical - TRUE Add LOWESS line to scatter plots

Examples

library(smooth)

# Fit model
model <- adam(AirPassengers, "MMM", lags=12, h=12, holdout=TRUE)

# Quick diagnostics (default plots)
plot(model)

# Full diagnostic suite
par(mfcol=c(3,4))
plot(model, which=1:11)

# Decomposition view
par(mfcol=c(1,1))
plot(model, which=12)

summary()

Provides a detailed summary including parameter estimates with standard errors and confidence intervals.

Note: Not yet implemented in Python.

R Usage

model <- adam(AirPassengers, "MMM", lags=12, h=12, holdout=TRUE)
summary(model)

Output Contents

The summary includes:

  • Model specification
  • Time elapsed
  • Loss value and information criteria
  • Parameter estimates with:
    • Estimate value
    • Standard error
    • Lower confidence interval
    • Upper confidence interval
  • Degrees of freedom

Example

model <- adam(BJsales, "AAN", h=12, holdout=TRUE)
summary(model)

Output:

Model estimated using adam() function: ETS(AAN)
Response variable: BJsales
Distribution used in the estimation: Normal
Loss function type: likelihood; Loss function value: 240.6045
Coefficients:
      Estimate Std. Error Lower 2.5% Upper 97.5%  
alpha   1.0000     0.0966     0.8090      1.0000 *
beta    0.2437     0.0802     0.0851      0.4023 *

Error standard deviation: 1.3936
Sample size: 138
Number of estimated parameters: 3
Number of degrees of freedom: 135
Information criteria:
     AIC     AICc      BIC     BICc 
487.2090 487.3881 495.9908 496.4320

Note on Standard Errors

Standard errors are computed using the Fisher Information matrix, which is computationally expensive. For models with many parameters (>30), this calculation may take considerable time. Also, the success of the computation of this depends on how close the loss function value was to the optimum in the estimation.

xtable()

Creates LaTeX table output from the model summary. Useful for academic papers and reports.

Note: Not yet implemented in Python.

R Usage

library(xtable)

model <- adam(BJsales, "AAN", lags=12, h=12, holdout=TRUE)
modelSummary <- summary(model)

# Generate LaTeX table
xtable(modelSummary)

Output

Produces LaTeX code that can be included directly in documents:

% latex table generated in R 4.5.1 by xtable 1.8-4 package
% Fri Jan 30 09:54:58 2026
\begin{table}[ht]
\centering
\begin{tabular}{rrrrr}
  \hline
 & Estimate & Std. Error & Lower 2.5\% & Upper 97.5\% \\ 
  \hline
alpha & 1.0000 & 0.0966 & 0.81 & 1.0000 \\ 
  beta & 0.2437 & 0.0802 & 0.09 & 0.4023 \\ 
   \hline
\end{tabular}
\end{table}

Forecast Plotting

Plot forecasts with prediction intervals using the forecast() function output.

Note: Not yet implemented in Python.

R Usage

model <- adam(AirPassengers, "MMM", lags=12, h=12, holdout=TRUE)

# Generate forecast
modelForecast <- forecast(model, h=24, interval="prediction")

# Plot forecast
plot(modelForecast)

# Multiple confidence levels
modelForecast <- forecast(model, h=24, interval="semiparametric", level=c(0.9, 0.95))
plot(modelForecast)

See Also

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