Confidence intervals

Confidence intervals

Usage

confint_filter(
  x,
  coef,
  coef_var = coef,
  level = 0.95,
  asymmetric_var = TRUE,
  gaussian_distribution = FALSE,
  exact_df = TRUE,
  ...
)

Arguments

x

input time series.

coef

moving-average (moving_average()) or finite filter (finite_filters()) used to filter the series.

coef_var

moving-average (moving_average()) or finite filter (finite_filters()) used compute the variance (throw var_estimator()). By default equal to coef.

level

confidence level.

asymmetric_var

if asymmetric_var = TRUE then the variance is estimated for each asymmetric filters instead of using the variance associated the symmetric estimates.

gaussian_distribution

if TRUE use the normal distribution to compute the confidence interval, otherwise use the t-distribution.

exact_df

if TRUE compute the exact degrees of freedom for the t-distribution (when gaussian_distribution = FALSE), otherwise uses an approximation.

...

other arguments passed to the function moving_average() to convert coef to a "moving_average" object.

Details

Let \((\theta_i)_{-p\leq i \leq q}\) be a moving average of length \(p+q+1\) used to filter a time series \((y_i)_{1\leq i \leq n}\). Let denote \(\hat{\mu}_t\) the filtered series computed at time \(t\) as: $$ \hat{\mu}_t = \sum_{i=-p}^q \theta_i y_{t+i}. $$ If \(\hat{\mu}_t\) is unbiased, a approximate confidence for the true mean is: $$ \left[\hat{\mu}_t - z_{1-\alpha/2} \hat{\sigma} \sqrt{\sum_{i=-p}^q\theta_i^2}; \hat{\mu}_t + z_{1-\alpha/2} \hat{\sigma} \sqrt{\sum_{i=-p}^q\theta_i^2} \right], $$ where \(z_{1-\alpha/2}\) is the quantile \(1-\alpha/2\) of the standard normal distribution.

The estimate of the variance \(\hat{\sigma}\) is obtained using var_estimator() with the parameter coef_var. The assumption that \(\hat{\mu}_t\) is unbiased is rarely exactly true, so variance estimates and confidence intervals are usually computed at small bandwidths where bias is small.

When coef (or coef_var) is a finite filter, the last points of the confidence interval are computed using the corresponding asymmetric filters

References

Loader, Clive. 1999. Local regression and likelihood. New York: Springer-Verlag.

Examples

x <- retailsa$DrinkingPlaces
coef <- lp_filter(6)
#> Error in .jcall("jdplus/filters/base/r/LocalPolynomialFilters", "Ljdplus/toolkit/base/core/math/linearfilters/ISymmetricFiltering;",     "filters", as.integer(horizon), as.integer(degree), kernel,     endpoints, d, tweight, passband): RcallMethod: cannot determine object class
confint <- confint_filter(x, coef)
#> Error in UseMethod("finite_filters", sfilter): no applicable method for 'finite_filters' applied to an object of class "function"
plot(confint, plot.type = "single",
     col = c("red", "black", "black"),
     lty = c(1, 2, 2))
#> Error in object$coefficients: $ operator is invalid for atomic vectors