| Type: | Package |
| Title: | Point Process Time Series |
| Version: | 1.0 |
| Date: | 2026-05-09 |
| Author: | Daniel Gervini [aut, cre], Simon Kopischke [aut] |
| Maintainer: | Daniel Gervini <gervini@uwm.edu> |
| Description: | Provides functions for point process time series. Autocorrelation functions for spatial and temporal time series, and estimation of trend-plus-seasonality models for temporal and spatial time series. See Gervini (2025) <doi:10.1111/jtsa.70018> and Gervini and Kopischke (2026) <doi:10.48550/arXiv.2605.21884>. |
| License: | MIT + file LICENSE |
| LazyData: | true |
| NeedsCompilation: | no |
| Depends: | R (≥ 3.5.0) |
| Packaged: | 2026-05-23 03:05:56 UTC; simonkopischke |
| Repository: | CRAN |
| Date/Publication: | 2026-05-29 09:30:16 UTC |
PPTS
Description
Functions for analysis of temporal and spatial point process time series.
Details
Functions for autocorrelation estimation: acf_tPP, acf_sPP.
Functions for estimation of trend-plus-seasonality models: trend_seas_t, trend_seas_s.
Data sets "bikes" and "crime" are also included.
Author(s)
Daniel Gervini and Simon A. Kopischke
Maintainer: Simon A. Kopischke
References
Gervini, D. (2025). Autocorrelation functions for point-process time series. Journal of Time Series Analysis. DOI: 10.1111/jtsa.70018.
Gervini, D. and Kopischke, S.A. (2026). Trend and seasonality estimation for point-process time series. DOI: 10.48550/arXiv.2605.21884.
NSF DMS 2412015: "Statistical methods for point-process time series".
Autocorrelogram for spatial point-process time series
Description
Spatial binned autocorrelograms.
Usage
acf_sPP(x, rng, kmax = 10*log10(length(x)), nbin = 9,
alpha = 0.05, MC = 10000, no.plot = FALSE)
Arguments
x |
(n-list) Observations (x[[i]] is a mi x 2 matrix, possibly mi=0, first column is longitude, second column is latitude) |
rng |
(4-vector) Spatial range of the process (first two numbers are longitude range, the other two are latitude range) |
kmax |
(int>=0) Maximum lag (default 10*log10(n)) |
nbin |
(int>=4) Number of bins for binned estimator (default 9) (if not a perfect square integer, the closest perfect square is used) |
alpha |
(scalar) Significance test level |
MC |
(integer) Number of Monte Carlo replications for significance threshold computation (Default 10,000. Use MC=0 if no threshold computation is desired) |
no.plot |
(logical) Plot is shown if FALSE (default) |
Value
lag |
(kmax-vector) Lags at which autocorrelations are computed (1:kmax) |
rho |
(kmax-vector) Autocorrelations at lags 1:kmax |
thr |
(scalar) Significance threshold |
Author(s)
Daniel Gervini
References
Gervini, D. (2025), "Autocorrelation functions for point-process time series", Journal of Time Series Analysis, DOI: 10.1111/jtsa.70018
Examples
data(crime)
acf_sPP(x=crime$x,rng=crime$range)
Autocorrelogram for temporal point-process time series
Description
Temporal binned autocorrelograms.
Usage
acf_tPP(x, rng, kmax = 10*log10(length(x)), nbin = 5,
alpha = 0.05, MC = 10000, no.plot = FALSE)
Arguments
x |
(n-list) Observations (x[[i]] is a vector of length mi, possibly mi=0) |
rng |
(2-vector) Time range of the process |
kmax |
(int>=0) Maximum lag (default 10*log10(n)) |
nbin |
(int>=0) Number of bins for binned estimator (default 5) |
alpha |
(scalar) Significance test level |
MC |
(integer) Number of Monte Carlo replications for significance threshold computation (Default 10,000. Use MC=0 if no threshold computation is desired) |
no.plot |
(logical) Plot is shown if FALSE (default) |
Value
lag |
(kmax-vector) Lags at which autocorrelations are computed (1:kmax) |
rho |
(kmax-vector) Autocorrelations at lags 1:kmax |
thr |
(scalar) Significance threshold |
Author(s)
Daniel Gervini
References
Gervini, D. (2025), "Autocorrelation functions for point-process time series", Journal of Time Series Analysis, DOI: 10.1111/jtsa.70018
Examples
data(bikes)
acf_tPP(x=bikes$x,rng=bikes$range)
Divvy Bike Rides
Description
Daily bicycle check-out times (Jan 1, 2016 to Dec 31, 2016) at Ashland & Wrightwood station of the Divvy bike-sharing system in the city of Chicago.
Usage
data("bikes")Format
A list with two elements: range (vector of length 2) and x (list of length 366).
Details
Vector bikes$range indicates time range used for some (but not all) analyses in the paper. List bikes$x contains the daily bike check-out times as vectors, with time given in hours in the [0,24) range.
Source
Chicago Data Portal, https://data.cityofchicago.org/
References
Gervini, D. (2025). Autocorrelation functions for point-process time series. Journal of Time Series Analysis. DOI: 10.1111/jtsa.70018.
Gervini, D. and Kopischke, S.A. (2026). Trend and seasonality estimation for point-process time series. DOI: 10.48550/arXiv.2605.21884
NSF DMS 2412015: "Statistical methods for point-process time series".
Examples
require(PPTS)
data(bikes)
oldpar <- par(no.readonly = TRUE)
fit <- trend_seas_t(x=bikes$x,rng=c(4,24),d=7,c.deg=3,sp.nk=5,maxit=10000)
par(mfrow=c(2,1),mar=c(4,4,1,1),mgp=c(2,1,0))
plot(fit$tt,exp(fit$ct),type="l",xlab="t (day)",ylab="exp(c(t))")
title(main="Multiplicative trend")
matplot(fit$u,exp(fit$mus),type="l",lty=1,xlab="u (hour)",ylab=expression(nu[j](u)))
title(main="Baseline seasonal intensities")
par(oldpar)
Chicago Street Theft
Description
Daily street theft locations in the North side of Chicago for the year 2014.
Usage
data("crime")Format
A list with two elements: range (vector of length 4) and x (list of length 365).
Details
Vector crime$range (W longitude, E longitude, S latitude, N latitude) indicates spatial range used for the analyses in the paper.
List crime$x contains locations of daily incidents in matrix form (each row corresponds to a different incident, columns are longitude-latitude coordinates)
Source
Chicago Data Portal, https://data.cityofchicago.org/
References
Gervini, D. (2025). Autocorrelation functions for point-process time series. Journal of Time Series Analysis. DOI: 10.1111/jtsa.70018.
Gervini, D. and Kopischke, S.A. (2026). Trend and seasonality estimation for point-process time series. DOI: 10.48550/arXiv.2605.21884
NSF DMS 2412015: "Statistical methods for point-process time series".
Examples
require(PPTS)
data(crime)
fit <- trend_seas_s(x=crime$x,rng=crime$range,d=1,c.deg=3,sp.nk=3,maxit=10000)
plot(fit$t,exp(fit$c),type="l",,xlab="t (day)",ylab="exp(c(t))")
title(main="Multiplicative trend")
filled.contour(fit$u1,fit$u2,exp(fit$mu[,,1]))
title(main=expression(paste("Baseline intensity ",nu(u))),xlab="Longitude",ylab="Latitude")
Trend and seasonality estimation for spatial Point Process Time Series
Description
Fits seasonal additive model \mu(u,t) = c(t) + \mu_{j(t)}(u)
to log-intensity process \log(\Lambda_{t}(u)), where c(t)
is a polynomial and \mu_1(u),\ldots,\mu_d(u) are tensor-product splines.
Usage
trend_seas_s(x, rng, d = 1, r = length(x) - length(x)%%d, c.deg = 1,
sp.nk = 1, sp.deg = 3, maxit = 100, conf = 0.95)
Arguments
x |
(n-list) Observations (x[[i]] is a mi x 2 matrix, possibly mi=0, first column is longitude, second column is latitude) |
rng |
(4-vector) Spatial range of the process (first two numbers are longitude range, the other two are latitude range) |
d |
(integer) Seasonal period (use default 1 for non-seasonal model) |
r |
(integer) Period of trend c(t) (must be a multiple of d; default is n-n%%d) |
c.deg |
(integer) Degree of polynomial c(t) |
sp.nk |
(integer) Number of spline knots per dimension for mu_j(u) |
sp.deg |
(integer) Spline degree for mu_j(u) |
maxit |
(integer) Maximum number of iterations |
conf |
(scalar) Confidence interval level (default is 0.95) |
Value
u1 |
(ng-vector) Grid for evaluation of mu_j(u) (longitude) |
u2 |
(ng-vector) Grid for evaluation of mu_j(u) (latitude) |
mus |
(ng x ng x d -array) Seasonal means mu_j(u) evaluated at u1 x u2 ( mus[i,k,j] = mu_j(u1[i],u2[k]) ) |
t |
(vector) Grid for evaluation of c(t) (t = 1:n) |
c |
(vector) Trend c(t) evaluated at t |
tt |
(vector) Grid for evaluation of one cycle of c(t) (tt = 1:r) |
ct |
(vector) One cycle of trend c(t) evaluated at tt |
eta |
(vector) Basis coefficients for c(t) |
thetas |
(matrix) Basis coefficients for mu_j(u) (in rows) |
ub_ct |
(vector) Upper conf bound for c(t) |
lb_ct |
(vector) Lower conf bound for c(t) |
ub_ect |
(vector) Upper conf bound for exp(c(t)) |
lb_ect |
(vector) Lower conf bound for exp(c(t)) |
ub_mus |
(ng x ng x d -array) Upper conf bound for mu_j(u)'s evaluated at u1 x u2 |
lb_mus |
(ng x ng x d -array) Lower conf bound for mu_j(u)'s evaluated at u1 x u2 |
ub_lmb |
(ng x ng x d -array) Upper conf bound for exp(mu_j(u))'s evaluated at u1 x u2 |
lb_lmb |
(ng x ng x d -array) Lower conf bound for exp(mu_j(u))'s evaluated at u1 x u2 |
Omega |
(matrix) Covariance matrix of joint parameters |
Author(s)
Daniel Gervini
References
Gervini, D., and Kopischke, S.A. (2006), "Trend and seasonality estimation for point-process time series." DOI: 10.48550/arXiv.2605.21884
Examples
data(crime)
fit <- trend_seas_s(x=crime$x,rng=crime$range,d=7,c.deg=3,sp.nk=3)
plot(fit$t,fit$c,type="l")
filled.contour(fit$u1,fit$u2,exp(fit$mus[,,1]))
Trend and seasonality estimation for temporal Point Process Time Series
Description
Fits seasonal additive model \mu(u,t) = c(t) + \mu_{j(t)}(u)
to log-intensity process \log(\Lambda_{t}(u)),
where c(t) is a polynomial and \mu_1(u),\ldots,\mu_d(u)
are splines.
Usage
trend_seas_t(x, rng, d = 1, r = length(x) - length(x)%%d, c.deg = 1,
sp.nk = 1, sp.deg = 3, maxit = 100, conf = 0.95)
Arguments
x |
(n-list) Observations (x[[i]] is a vector of length mi, possibly mi=0) |
rng |
(vector, length 2) Time range of the process |
d |
(integer) Seasonal period (use default 1 for non-seasonal model) |
r |
(integer) Period of trend c(t) (must be a multiple of d; default is n-n%%d) |
c.deg |
(integer) Degree of polynomial c(t) |
sp.nk |
(integer) Number of spline knots for mu_j(u) |
sp.deg |
(integer) Spline degree for mu_j(u) |
maxit |
(integer) Maximum number of iterations |
conf |
(scalar) Confidence interval level (default is 0.95) |
Value
u |
(vector) Grid for evaluation of mu_j(u) |
mus |
(matrix) Seasonal means mu_j(u) (in columns) evaluated at u |
t |
(vector) Grid for evaluation of c(t) (t = 1:n) |
c |
(vector) Trend c(t) evaluated at t |
tt |
(vector) Grid for evaluation of one cycle of c(t) (tt = 1:r) |
ct |
(vector) One cycle of trend c(t) evaluated at tt |
eta |
(vector) Basis coefficients for c(t) |
thetas |
(matrix) Basis coefficients for mu_j(u) (in rows) |
ub_ct |
(vector) Upper conf bound for c(t) |
lb_ct |
(vector) Lower conf bound for c(t) |
ub_ect |
(vector) Upper conf bound for exp(c(t)) |
lb_ect |
(vector) Lower conf bound for exp(c(t)) |
ub_mus |
(matrix) Upper conf bound for mu_j(u) (in columns) |
lb_mus |
(matrix) Lower conf bound for mu_j(u) (in columns) |
ub_lmb |
(matrix) Upper conf bound for exp(mu_j(u)) (in columns) |
lb_lmb |
(matrix) Lower conf bound for exp(mu_j(u)) (in columns) |
Omega |
(matrix) Covariance matrix of joint parameters |
Author(s)
Daniel Gervini
References
Gervini, D., and Kopischke, S.A. (2006), "Trend and seasonality estimation for point-process time series." DOI: 10.48550/arXiv.2605.21884
Examples
data(bikes)
fit <- trend_seas_t(x=bikes$x,rng=bikes$range,d=7,c.deg=3,sp.nk=5)
plot(fit$tt,fit$ct,type="l")
matplot(fit$u,exp(fit$mus),type="l",lty=1)