Check the validity of the neighbourhood specification

Description

Check the validity of the neighbourhood specification

Usage

check_nbd(nbd_info)

Arguments

Value

No return value. Show an error message if nbd_info is invalid.

Examples

nbd_info <- list(c(1:10),c(8:20))
check_nbd <- check_nbd(nbd_info)

U.S. COVID-19 Data

Description

Daily number of COVID-19 cases for 58 areas in the United States (including 50 states, Washington D.C., 5 territories and 2 cruise ships) for 812 days from 22 Jan 2020 to 12 April 2022.

Usage

covid_data

Format

covid_data

A data matrix with p = 58 rows and n = 812 columns.

Source

U.S. CDC https://covid.cdc.gov/covid-data-tracker/#maps_new-admissions-rate-county

U.S. COVID-19 Data Neighbourhood Information

Description

U.S. COVID-19 Data Neighbourhood Information

Usage

covid_nbd_info

Format

covid_nbd_info

A list containing five arrays indicating the constituents of five U.S. regions:

Northeast: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, Vermont, New Jersey, New York, and Pennsylvania.

Midwest: Illinois, Indiana, Michigan, Ohio, Wisconsin, Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota.

South: Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, District of Columbia, West Virginia, Alabama, Kentucky, Mississippi, Tennessee, Arkansas, Louisiana, Oklahoma, and Texas.

West: Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, Wyoming, Alaska, California, Hawaii, Oregon, and Washington.

Others: American Samoa, Diamond Princess, Grand Princess, Guam, Northern Mariana Islands, Puerto Rico, and Virgin Islands.

Source

U.S. Census Bureau, W. (2000). List of regions of the United States.

Construct an S3 class 'no_nbd' or 'nbd' for change-point estimation

Description

Construct an S3 class 'no_nbd' or 'nbd' for change-point estimation

Usage

est_hdchange(hdobj, test_stats, threshold, stat_all, critical_values)

Arguments

Value

An S3 object of class 'no_nbd' or 'nbd' used as the argument of get_breaks().

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

teststats <- get_teststats(ts_no_nbd)
V_12_MAinf <- get_V_l2_MAinf(ts_no_nbd)

estobj <- est_hdchange(hdobj = ts_no_nbd, test_stats = teststats$stat_max,
threshold = 1e-5, stat_all = V_12_MAinf, critical_values = c(0.01, 0.05, 0.1))

Generate a random Gaussian vector

Description

Generate a random Gaussian vector

Usage

genZ(hdobj)

Arguments

Value

The Gaussian random vector \mathcal{Z}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

Z <- genZ(ts_no_nbd)

Obtain the simulated standardised gap vector

Description

Obtain the simulated standardised gap vector

Usage

get_GS_MAinf(hdobj)

Arguments

Value

An array of the simulated counterpart of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

GS_MAinf <- get_GS_MAinf(ts_no_nbd)

Obtain the simulated standardised gap vector

Description

Obtain the simulated standardised gap vector

Usage

## S3 method for class 'nbd'
get_GS_MAinf(hdobj)

Arguments

Value

An array of the simulated counterpart of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the simulated standardised gap vector

Description

Obtain the simulated standardised gap vector

Usage

## S3 method for class 'no_nbd'
get_GS_MAinf(hdobj)

Arguments

Value

An array of the simulated counterpart of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the standardised gap vector

Description

Obtain the standardised gap vector

Usage

get_V_l2_MAinf(hdobj)

Arguments

Value

An array of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

V_12_MAinf <- get_V_l2_MAinf(ts_no_nbd)

Obtain the standardised gap vector

Description

Obtain the standardised gap vector

Usage

## S3 method for class 'nbd'
get_V_l2_MAinf(hdobj)

Arguments

Value

An array of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the standardised gap vector

Description

Obtain the standardised gap vector

Usage

## S3 method for class 'no_nbd'
get_V_l2_MAinf(hdobj)

Arguments

Value

An array of |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the time-stamps and spatial locations with breaks

Description

Obtain the time-stamps and spatial locations with breaks

Usage

get_breaks(estobj)

Arguments

Value

A list containing the time-stamps and spatial locations with breaks. For S3 class 'no_nbd', it returns the total number of breaks \widehat{K} and the time-stamps \hat{\tau}_{k}. See Algorithm 1 of Li et al. (2023). For S3 class 'nbd', it returns the total number of breaks \widehat{R} and the spatial-temporal location of the break (\hat{\tau}_{r},\hat{s}_{r}). See Algorithm 2 of Li et al. (2023).

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

teststats <- get_teststats(ts_no_nbd)
V_12_MAinf <- get_V_l2_MAinf(ts_no_nbd)

estobj <- est_hdchange(hdobj = ts_no_nbd, test_stats = teststats$stat_max,
threshold = 1e-5, stat_all = V_12_MAinf, critical_values = c(0.01, 0.05, 0.1))

breaks <- get_breaks(estobj)

Obtain the time-stamps and spatial locations with breaks

Description

Obtain the time-stamps and spatial locations with breaks

Usage

## S3 method for class 'nbd'
get_breaks(estobj)

Arguments

Value

A list containing the total number of breaks \widehat{R} and the spatial-temporal location of the break (\hat{\tau}_{r},\hat{s}_{r}). See Algorithm 2 of Li et al. (2023).

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the time-stamps and spatial locations without break

Description

Obtain the time-stamps and spatial locations without break

Usage

## S3 method for class 'no_nbd'
get_breaks(estobj)

Arguments

Value

A list containing the total number of breaks \widehat{K} and the time-stamps \hat{\tau}_{k}. See Algorithm 1 of Li et al. (2023).

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

The covariance matrix for generating random Gaussian vector

Description

The covariance matrix for generating random Gaussian vector

Usage

get_cov_x_MAinf(n, b)

Arguments

Value

The covariance matrix. See section 2.2 of Li et al. (2023).

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

Cov_x_MAinf <- get_cov_x_MAinf(ts_no_nbd$n, ts_no_nbd$b)

Obtain critical values and threshold

Description

Obtain critical values and threshold

Usage

get_critical(hdobj)

Arguments

Value

A list containing the critical values and the threshold parameter \omega.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

crit <- get_critical(ts_no_nbd)

Obtain critical values and threshold

Description

Obtain critical values and threshold

Usage

## S3 method for class 'nbd'
get_critical(hdobj)

Arguments

Value

A list containing the critical values and the threshold parameter \omega.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain critical values and threshold

Description

Obtain critical values and threshold

Usage

## S3 method for class 'no_nbd'
get_critical(hdobj)

Arguments

Value

A list containing the critical values and the threshold parameter \omega.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Compute the long-run variance of the gap vector

Description

Compute the long-run variance of the gap vector

Usage

get_lr_var(hdobj)

Arguments

Value

The covariance matrix of the gap vectors \hat{J}(.).

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

lr_var <- get_lr_var(ts_no_nbd)

Obtain the test statistics

Description

Obtain the test statistics

Usage

get_teststats(hdobj)

Arguments

Value

A list containing the test statistics \mathcal{\boldsymbol{Q}}_{n} and a sequence of standardised |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

teststat <- get_teststats(ts_no_nbd)

Obtain the test statistics

Description

Obtain the test statistics

Usage

## S3 method for class 'nbd'
get_teststats(hdobj)

Arguments

Value

A list containing the test statistics \mathcal{\boldsymbol{Q}}_{n} and a sequence of standardised |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Obtain the test statistics

Description

Obtain the test statistics

Usage

## S3 method for class 'no_nbd'
get_teststats(hdobj)

Arguments

Value

A list containing the test statistics \mathcal{\boldsymbol{Q}}_{n} and a sequence of standardised |V_{i}|_{2}^{2}.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Estimate the time-stamps and spatial locations with breaks

Description

The main function of this package. It performs a test for existence of breaks and estimates the time-stamps and locations of the breaks.

Usage

hdchange(hdobj)

Arguments

Value

The return value is an S3 object of class 'no_nbd' or 'nbd' containing a list of the test results and change-point locations.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

############ No neighbourhood case ############

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))



# Estimate the time-stamps of the breaks
est_result_no_nbd <- hdchange(ts_no_nbd)

# Summarize the results
summary(est_result_no_nbd)

# Plot the results
plot_result(est_result_no_nbd)
axis(1,
  at = est_result_no_nbd$time_stamps,
  labels = c("break 1", "break 2", "break 3")
)
title(main = "Change-points estimation")


############ Neighbourhood case ############

# generate data
data_nbd <- sim_hdchange_nbd(n = 300,
p = 70,
nbd_info =
 list(
   (1:9), (2:31), (32:41), (42:70),
   (3:15), (16:35), (31:55)
 ),
sp_tp_break = rbind(c(2, 50), c(4, 150), c(2, 250)),
dist_info =
  list(dist = "t", dependence = "iid", param = 5),
jump_max = 1)

# construct nbd object
ts_nbd <- ts_hdchange(data_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1),
nbd_info =
 list(
   (1:9), (2:31), (32:41), (42:70),
   (3:15), (16:35), (31:55)
 ))



# Estimate the time-stamps of the breaks
est_result_nbd <- hdchange(ts_nbd)

# Summarize the results
summary(est_result_nbd)

# Plot the results
plot_result(est_result_nbd, nbd_index = 2)
pairs <- est_result_nbd$nbd_and_stamps_pair
time_stamps <- pairs[pairs[, 1] == 2, 2]
axis(1,
  at = time_stamps,
  labels = c("break 1", "break 2")
)
title(main = "Change-points estimation for neibourhood 2")

Plot the time series and change-points

Description

Plot the time series and change-points

Usage

plot_result(est_result, ...)

Arguments

Details

See hdchange() for examples.

Value

No return value. Presents the plot of the data and breaks.

Examples

# generate data
data_nbd <- sim_hdchange_nbd(n = 300,
p = 70,
nbd_info =
 list(
   (1:9), (2:31), (32:41), (42:70),
   (3:15), (16:35), (31:55)
 ),
sp_tp_break = rbind(c(2, 50), c(4, 150), c(2, 250)),
dist_info =
  list(dist = "t", dependence = "iid", param = 5),
jump_max = 1)

# construct nbd object
ts_nbd <- ts_hdchange(data_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1),
nbd_info =
 list(
   (1:9), (2:31), (32:41), (42:70),
   (3:15), (16:35), (31:55)
 ))

# Estimate the time-stamps of the breaks
est_result_nbd <- hdchange(ts_nbd)

# Plot the results
plot_result(est_result_nbd, nbd_index = 2)
pairs <- est_result_nbd$nbd_and_stamps_pair
time_stamps <- pairs[pairs[, 1] == 2, 2]
axis(1,
  at = time_stamps,
  labels = c("break 1", "break 2")
)
title(main = "Change-points estimation for neibourhood 2")

Plot the time series and change-points

Description

Plot the time series and change-points

Usage

## S3 method for class 'result_nbd'
plot_result(est_result, ..., nbd_index)

Arguments

Details

See hdchange() for examples.

Value

No return value. Presents the plot of the data and breaks.

Plot the time series and change-points

Description

Plot the time series and change-points

Usage

## S3 method for class 'result_no_nbd'
plot_result(est_result, ...)

Arguments

Details

See hdchange() for examples.

Value

No return value. Presents the plot of the data and breaks.

Simulate data with neighbourhood

Description

Simulate data with neighbourhood

Usage

sim_hdchange_nbd(
  n = 300,
  p = 70,
  nbd_info = list((1:9), (2:31), (32:41), (42:70), (3:15), (16:35), (31:55)),
  sp_tp_break = rbind(c(2, 50), c(4, 150), c(2, 250)),
  dist_info = list(dist = "normal", dependence = "iid", param = 1),
  jump_max = 1
)

Arguments

Details

'sp_tp_break' should be a K \times 2 matrix with first column indicating the neighbourhoods and the second column indicating the time stamps. For example, 'sp_tp_break = rbind(c(2, 50), c(4, 150), c(2, 250))' means that the second neighbourhood has two breaks taking place at i = 50, 250 and the fourth neighbourhood has one break taking place at i = 150.

'dist_info' should be a list containing the following items:

• dist: distribution of the innovations, either "normal" or "t".

• dependence: iid or MA(\infty), either "iid" or "MA_inf".

• param = parameter of the distribution, standard deviation for normal distribution and degree of freedom for t distribution

'jump_max' is set equal in nbd case for convenience.

See ts_hdchange() for example.

Value

A p \times n simulated data matrix.

Examples

data_nbd <- sim_hdchange_nbd(n = 300,
p = 70,
nbd_info =
 list(
   (1:9), (2:31), (32:41), (42:70),
   (3:15), (16:35), (31:55)
 ),
sp_tp_break = rbind(c(2, 50), c(4, 150), c(2, 250)),
dist_info =
  list(dist = "t", dependence = "iid", param = 5),
jump_max = 1)

Simulate data without neighbourhood

Description

Simulate data without neighbourhood

Usage

sim_hdchange_no_nbd(
  n = 200,
  p = 30,
  S = 30,
  tau = c(40, 100, 160),
  dist_info = list(dist = "normal", dependence = "iid", param = 1),
  jump_max = c(2, 2, 1.5)
)

Arguments

Details

'dist_info' should be a list containing the following items:

• dist: distribution of the innovations, either "normal" or "t".

• dependence: iid or MA(\infty), either "iid" or "MA_inf".

• param = parameter of the distribution, standard deviation for normal distribution and degree of freedom for t distribution

See ts_hdchange() for example.

Value

A p \times n simulated data matrix.

Examples

data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

Summarize the estimation results

Description

Summarize the estimation results

Usage

## S3 method for class 'result_nbd'
summary(object, ...)

Arguments

Details

See hdchange() for examples.

Value

No return value. Presents the summary of the test and estimation results.

Summarize the estimation results

Description

Summarize the estimation results

Usage

## S3 method for class 'result_no_nbd'
summary(object, ...)

Arguments

Details

See hdchange() for examples.

Value

No return value. Presents the summary of the test and estimation results.

Test the existence of change-points in the data

Description

Test the existence of change-points in the data

Usage

test_existence(hdobj, display = TRUE)

Arguments

Details

See hdchange() for examples.

Value

A list containing the following elements:

• 'test_stats' The test statistics \mathcal{\boldsymbol{Q}}_{n}.

• 'critical_values' The critical values.

• 'stat_all' An array of |V_{i}|_{2}^{2}.

• 'critical_value_alpha' The threshold value \omega depending on alpha.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

# generate data
data_no_nbd <- sim_hdchange_no_nbd(n = 200,
p = 30,
S = 30,
tau = c(40, 100, 160),
dist_info =
  list(dist = "normal", dependence = "MA_inf", param = 1),
jump_max = c(2, 2, 1.5))

# construct no_nbd object
ts_no_nbd <- ts_hdchange(data_no_nbd,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

test <- test_existence(ts_no_nbd, display = TRUE)

'no_nbd' or 'nbd' object construction

Description

This function creates an S3 object of class 'no_nbd' or 'nbd' containing the initialising information supplied to the main function hdchange(). 'no_nbd' or 'nbd' are constructed depending on whether the neighbourhood information is provided. The resulting object will be used in the test and estimation functions.

Usage

ts_hdchange(
  data,
  window_size = 30,
  m = 8,
  h = 1,
  N_rep = 999,
  alpha = 1e-05,
  quantiles = c(0.01, 0.05, 0.1),
  nbd_info = NULL
)

Arguments

Details

'nbd_info' indicates the location of individuals in the data matrix. For example, 'nbd_info = list(c(1:10), c(25:35), c(7:18))' means that there are three neighbourhoods. The first neighbourhood contains from the 1st to 10th individuals and the same rule applies to the rest of neighbourhoods. The neighbourhoods are allowed to be overlapped. See also the illustrating example in hdchange().

Value

The return value is an S3 object of class 'no_nbd' or 'nbd'. It contains a list of the following items:

• data, m, h, N_rep, alpha, quantiles, and nbd_info are the same as in the arguments.

• n = number of time series observations.

• p = cross-sectional dimension.

• b = bandwith parameter b = window\_size/n.

References

Li, J., Chen, L., Wang, W. and Wu, W.B., 2022. \ell^2 Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM. arXiv preprint arXiv:2208.13074.

Examples

data <- covid_data

# No neighbourhood case
ts_no_nbd <- ts_hdchange(data,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1))

# Neighbourhood case
ts_nbd <- ts_hdchange(data,
window_size = 30,
m = 8,
h = 1,
N_rep = 999,
alpha = 1e-5,
quantiles = c(0.01, 0.05, 0.1),
nbd_info = list(c(1:10), c(25:35), c(7:18)))