Non-stationary Cosinor

Decompose a time series using a non-stationary cosinor for the seasonal pattern.

Usage

nscosinor(
  data,
  response,
  cycles,
  niters = 1000,
  burnin = 500,
  tau,
  lambda = 1/12,
  div = 50,
  monthly = TRUE,
  alpha = 0.05,
  year_col = "year",
  month_col = "month"
)

Arguments

data: Data frame. Assumes no missing data. Year and month columns are by default assumed to be "year", and "month", respectively. These can be specified with arguments year_col and month_col.
response: character. Response variable.
cycles: vector of cycles in units of time, e.g., for a six and twelve month pattern cycles=c(6,12).
niters: total number of MCMC samples (default=1000).
burnin: number of MCMC samples discarded as a burn-in (default=500).
tau: vector of smoothing parameters, tau[1] for trend, tau[2] for 1st seasonal parameter, tau[3] for 2nd seasonal parameter, etc. Larger values of tau allow more change between observations and hence a greater potential flexibility in the trend and season.
lambda: distance between observations (lambda=1/12 for monthly data, default).
div: divisor at which MCMC sample progress is reported (default=50).
monthly: TRUE for monthly data.
alpha: Statistical significance level used by the confidence intervals.
year_col: character. column referring to year. Default is "year".
month_col: character. column referring to month. Default is "month".

Value

Returns an object of class "nsCosinor" with the following parts:

call: the original call to the nscosinor function.
time: the year and month for monthly data.
trend: mean trend and 95\
season: mean season(s) and 95\
oseason: overall season(s) and 95\ be the same as season if there is only one seasonal cycle.
fitted: fitted values and 95\ season(s).
residuals: residuals based on mean trend and season(s).
n: the length of the series.
chains: MCMC chains (of class mcmc) of variance estimates: standard error for overall noise (std.error), standard error for season(s) (std.season), phase(s) and amplitude(s).
cycles: vector of cycles in units of time.

Details

This model is designed to decompose an equally spaced time series into a trend, season(s) and noise. A seasonal estimate is estimated as \(s_t=A_t\cos(\omega_t-P_t)\), where t is time, \(A_t\) is the non-stationary amplitude, \(P_t\) is the non-stationary phase and \(\omega_t\) is the frequency.

A non-stationary seasonal pattern is one that changes over time, hence this model gives potentially very flexible seasonal estimates.

The frequency of the seasonal estimate(s) are controlled by cycle. The cycles should be specified in units of time. If the data is monthly, then setting lambda=1/12 and cycles=12 will fit an annual seasonal pattern. If the data is daily, then setting lambda= 1/365.25 and cycles=365.25 will fit an annual seasonal pattern. Specifying cycles= c(182.6,365.25) will fit two seasonal patterns, one with a twice-annual cycle, and one with an annual cycle.

The estimates are made using a forward and backward sweep of the Kalman filter. Repeated estimates are made using Markov chain Monte Carlo (MCMC). For this reason the model can take a long time to run. To give stable estimates a reasonably long sample should be used (niters), and the possibly poor initial estimates should be discarded (burnin).

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer. doi:10.1007/978-3-642-10748-1

Barnett, A.G., Dobson, A.J. (2004) Estimating trends and seasonality in coronary heart disease Statistics in Medicine. 23(22) 3505–23.

Author

Adrian Barnett a.barnett@qut.edu.au

Examples

# \donttest{
# model to fit an annual pattern to the monthly cardiovascular disease data
f <- c(12)
tau <- c(10,50)
if (FALSE) { # \dontrun{
  res12 <- nscosinor(
    data = CVD,
    response = 'adj',
    cycles = f,
    niters = 200,
    burnin = 50,
    tau = tau
    )
summary(res12)
# autoplot replaces plot method - plot(res12)
autoplot(res12)
} # }
# }