nscosinor {season}

Non-stationary Cosinor

Description

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
)

Arguments

data

a data frame.

response

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.

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).

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% confidence interval.

season

mean season(s) and 95% confidence interval(s).

oseason

overall season(s) and 95% confidence interval(s). This will be the same as season if there is only one seasonal cycle.

fitted

fitted values and 95% confidence interval, based on trend + 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.

Author(s)

Adrian Barnett [e-mail]

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

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

See Also

plot.nsCosinor, summary.nsCosinor

Examples

data(CVD)
# model to fit an annual pattern to the monthly cardiovascular disease data
f = c(12)
tau = c(10,50)
## Not run: res12 = nscosinor(data=CVD, response='adj', cycles=f, niters=5000,
         burnin=1000, tau=tau)
summary(res12)
plot(res12)

## End(Not run)