Function that estimates the standard Bass model. Fitted values for cumulative and instantaneous data are displayed (if display = T). Out-of-sample prediction is performed based on estimated parameters.
BM(series, method = "nls", prelimestimates = c(sum(series) + 100, 0.01, 0.1),
oos = round(length(series)*0.25), alpha = 0.05 ,display = T)BM returns an object of class "Dimora".
The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by BM.
An object of class "Dimora" is a list containing at least the following components:
the model formula used.
the model frame used.
a summary table of estimates.
a named vector of coefficients.
the statistical measure R-squared.
the residual sum of squares.
the residuals (observed cumulative data - fitted cumulative data).
the cumulative fitted values.
the cumulative observed series.
the matched call.
the instantaneous observed data.
the estimation method, 'nlm' or 'optim' (see Details).
a vector containing the starting values used by the algorithm to estimate the parameters. If no values are specified, the default ones are:
innovation coefficient: \(p = 0.01\);
imitation coefficient: \(q = 0.1\).
the significance level for the confidence intervals.
positive integer value: number of predictions after the last observed one. Default setting to 25% of the length of the data.
if TRUE returns the fitted values for cumulative and instantaneous observed data. If 'oos' is specified, it also returns the predicted fit values.
Zanghi Federico: federico.zanghi.11@gmail.com
Savio Andrea: svandr97@gmail.com
Ziliotto Filippo: filippo.ziliotto1996@gmail.com
Bessi Alessandro: alessandrobessi92@gmail.com
The optim method provides only the parameter estimates. It does not provide the standard error and the p-value estimates.
Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.
Bass, F.M. (1969). A new product growth for model consumer durables. Management science, 15 (5), 215-227.
The Dimora models: GBM, GGM, UCRCD.
summary.Dimora for summaries.
plot.Dimora for graphics and residuals analysis.
predict.Dimora for prediction.
make.instantaneous to create instantaneous series from the cumulative one.
data(DBdimora)
iphone <- DBdimora$iPhone[7:52]
## Example 1
M1 <- BM(iphone)
summary(M1)
plot.Dimora(M1)
plot.Dimora(M1, oos=25)
# 25 predictions
## Example 2
M2 <- BM(iphone, prelimestimates = c(2000, 0.001, 0.1), method = "optim", oos = 100)
summary(M2)
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