sync_cluster: Time Series Clustering based on Trend Synchronism

In funtimes: Functions for Time Series Analysis

Time Series Clustering based on Trend Synchronism

Description

Cluster time series with a common parametric trend using the sync_test function \insertCiteLyubchich_Gel_2016_synchronism,Ghahari_etal_2017_MBDCEfuntimes.

Usage

sync_cluster(formula, rate = 1, alpha = 0.05, ...)

Arguments

formula	an object of class "formula", specifying the type of common trend for clustering the time series in a T by N matrix of time series (time series in columns) which is passed to sync_test. Variable t should be used to specify the form of the trend, where t is specified within the function automatically as a regular sequence of length T on the interval (0,1]. See Examples.
rate	rate of removal of time series. Default is 1 (i.e., if the hypothesis of synchronism is rejected one time series is removed at a time to re-test the remaining time series). Integer values above 1 are treated as the number of time series to be removed. Values from 0 to 1 are treated as a fraction of the time series to be removed.
alpha	significance level for testing the hypothesis of a common trend (using sync_test) of the parametric form specified in the formula.
...	arguments to be passed to sync_test, for example, number of bootstrap replications (B).

Details

The sync_cluster function recursively clusters time series having a pre-specified common parametric trend until there is no time series left. Starting with the given N time series, the sync_test function is used to test for a common trend. If the null hypothesis of common trend is not rejected by sync_test, the time series are grouped (i.e., assigned to a cluster). Otherwise, the time series with the largest contribution to the test statistics are temporarily removed (the number of time series to remove depends on the rate of removal), and sync_test is applied again. The contribution to the test statistic is assessed by the WAVK test statistic calculated for each time series.

Value

A list with the elements:

cluster	an integer vector indicating the cluster to which each time series is allocated. A label '0' is assigned to time series which do not have a common trend with other time series (that is, all time series labeled with '0' are separate one-element clusters).
elements	a list with names of the time series in each cluster.

The further elements combine results of sync_test for each cluster with at least two elements (that is, single-element clusters labeled with '0' are excluded):

estimate	a list with common parametric trend estimates obtained by sync_test for each cluster. The length of this list is max(cluster).
pval	a list of p-values of sync_test for each cluster. The length of this list is max(cluster).
statistic	a list with values of sync_test test statistic for each cluster. The length of this list is max(cluster).
ar_order	a list of AR filter orders used in sync_test for each time series. The results are grouped by cluster in the list of length max(cluster).
window_used	a list of local windows used in sync_test for each time series. The results are grouped by cluster in the list of length max(cluster).
all_considered_windows	a list of all windows considered in sync_test and corresponding test results, for each cluster. The length of this list is max(cluster).
WAVK_obs	a list of WAVK test statistics obtained in sync_test for each time series. The results are grouped by cluster in the list of length max(cluster).

Author(s)

Srishti Vishwakarma, Vyacheslav Lyubchich

References

\insertAllCited

See Also

BICC, DR, sync_test

Examples

## Not run: 
## Simulate 4 autoregressive time series, 
## 3 having a linear trend and 1 without a trend:
set.seed(123)
T = 100 #length of time series
N = 4 #number of time series
X = sapply(1:N, function(x) arima.sim(n = T, 
           list(order = c(1, 0, 0), ar = c(0.6))))
X[,1] <- 5 * (1:T)/T + X[,1]
plot.ts(X)

# Finding clusters with common linear trends:
LinTrend <- sync_cluster(X ~ t) 
  
## Sample Output:
##[1] "Cluster labels:"
##[1] 0 1 1 1
##[1] "Number of single-element clusters (labeled with '0'): 1"

## plotting the time series of the cluster obtained
for(i in 1:max(LinTrend$cluster)) {
    plot.ts(X[, LinTrend$cluster == i], 
            main = paste("Cluster", i))
}


## Simulating 7 autoregressive time series, 
## where first 4 time series have a linear trend added 
set.seed(234)
T = 100 #length of time series
a <- sapply(1:4, function(x) -10 + 0.1 * (1:T) + 
            arima.sim(n = T, list(order = c(1, 0, 0), ar = c(0.6))))
b <- sapply(1:3, function(x) arima.sim(n = T, 
            list(order = c(1, 0, 0), ar = c(0.6))))
Y <- cbind(a, b)
plot.ts(Y)

## Clustering based on linear trend with rate of removal = 2 
# and confidence level for the synchronism test 90%
LinTrend7 <- sync_cluster(Y ~ t, rate = 2, alpha = 0.1, B = 99)
   
## Sample output:
##[1] "Cluster labels:"
##[1] 1 1 1 0 2 0 2
##[1] "Number of single-element clusters (labeled with '0'): 2"

## End(Not run)

funtimes documentation built on March 31, 2023, 7:35 p.m.