Use time warping to reduce the number of observations in a month

Description

Reduce the number of observations in a month using time warping / stretching. Only relevant if a daily time series is simulated

Usage

.stretch_re(seas_component)

Arguments

Details

Usually time warping would be used to stretch the number of observations of a time series in a given interval to more observations. Here it is used to reduce the number of observations (31) to the number of days in a given month while maintaining the underlying trajectory of the data. This is done by first creating a very long time series for each month, interpolating missing values by spline interpolation and then reducing the number of observations to the number suitable for a given month.

Value

Returns a xts time series containing the day-of-the-month effect.

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Simulate calendar effects

Description

Simulate a time series containing specified calendar effects

Usage

sim_calendar(
  n,
  which = c("Easter", "Ascension"),
  from = 0,
  to = 0,
  freq = 12,
  effect_size = 3,
  start = "2020-01-01",
  multiplicative = TRUE,
  time_dynamic = 1,
  center = TRUE
)

Arguments

Details

If multiplicative is true, the effect size is measured in percentage. If is not true, the effect size is unit less and thus adopts the unit of the time series the calendars are added to. The time_dynamic parameter controls the change of the calendar effect. The effect of the previous year is multiplied by the time_dynamic factor.

Value

The function returns a time series of class xts

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Examples

plot(sim_calendar(60, from=0, to=4, freq=12))

Simulate a daily seasonal series

Description

Simulate a daily seasonal series as described in Ollech (2021).

Usage

sim_daily(
  N,
  sd = 5,
  moving = TRUE,
  week_sd = NA,
  month_sd = NA,
  year_sd = NA,
  week_change_sd = NA,
  month_change_sd = NA,
  year_change_sd = NA,
  innovations_sd = 1,
  sa_sd = NA,
  model = list(order = c(3, 1, 1), ma = 0.5, ar = c(0.2, -0.4, 0.1)),
  beta_tau7 = 0.01,
  beta_tau31 = 0,
  beta_tau365 = 0.2,
  start = c(2020, 1),
  multiplicative = TRUE,
  extra_smooth = FALSE,
  calendar = list(which = "Easter", from = -2, to = 2),
  outlier = NULL,
  timewarping = FALSE,
  as_index = FALSE
)

Arguments

Details

Standard deviation of the seasonal factor is in percent if a multiplicative time series model is assumed. Otherwise it is in unitless. Using a non-seasonal ARIMA model for the initialization of the seasonal factor does not impact the seasonality of the time series. It can just make it easier for human eyes to grasp the seasonal nature of the series. The definition of the ar and ma parameter needs to be inline with the chosen model. The parameters that can be set for calendar and outlier are those defined in sim_outlier and sim_calendar.

Value

Multiple simulated daily time series of class xts including:

original

The original series

seas_adj

The original series without calendar and seasonal effects

sfac7

The day-of-the-week effect

sfac31

The day-of-the-month effect

sfac365

The day-of-the-year effect

cfac

The calendar effects

outlier

The outlier effects

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Examples

x=sim_daily(5, sd=10, multiplicative=TRUE, outlier=list(k=5, type=c("AO", "LS")))
ts.plot(x[,1])

Simulate a daily time series based on the HS model

Description

This function simulates a daily time series with a Monte Carlo simulation based on an STS model based on Harvey and Shephard (1993) (HS model). The daily data consists of a trend, weekly seasonal, annual seasonal and irregular component. The components are each simulated by a transition process with daily random shocks. At the end of the simulation the components are combined and normalized to form the complete time series.

Usage

sim_daily_hs(
  N,
  multiplicative = TRUE,
  sizeWeeklySeas = 100,
  sizeAnnualSeas = 100,
  sizeTrend = 100,
  sizeDrift = 100,
  varIrregularity = 100,
  sizeWeeklySeasAux = 100,
  sizeAnnualSeasAux = 100,
  start = 2020,
  sizeBurnIn = 730,
  shockLevel = 1,
  shockDrift = 1,
  shockWeeklySeas = 1,
  shockAnnualSeas = 1,
  index = 100
)

Arguments

Details

The size of the components and the variance of the irregular component are defaulted to 100 each and the variances of the shocks are defaulted to 1.

The first effective year serves as base year for the time series

The impact of a seasonal factor on the time series depends on its ratio to the other components. To increase (decrease) a factor's impact, the value of the size needs to be increased (decreased) while the other components need to be kept constant. Therefore, the stability of the seasonal factor also grows as the shocks on the given component have less impact. In order to increase the impact without increasing the stability, the variance of the shock also needs to be raised accordingly.

Value

Multiple simulated daily time series of class xts including:

original

The original series

seas_adj

The original series seasonal effects

sfac7

The day-of-the-week effect

sfac365

The day-of-the-year effect

Author(s)

Nikolas Fritz , Daniel Ollech, based on code provided by Ángel Cuevas and Enrique M Quilis

References

Cuevas, Ángel and Quilis, Enrique M., Seasonal Adjustment Methods for Daily Time Series. A Comparison by a Monte Carlo Experiment (December 20, 2023). Available at SSRN: https://ssrn.com/abstract=4670922 or http://dx.doi.org/10.2139/ssrn.4670922

Structural Time Series (STS) Monte Carlo simulation Z = trend + seasonal_weekly + seasonal_annual + irregular, according to Harvey and Shephard (1993): "Structural Time Series Models", in Maddala, G.S., Rao, C.R. and Vinod, H.D. (Eds.) Handbook of Statistics, vol. 11, Elsevier Science Publishers.

Examples

x <- sim_daily_hs(4)
ts.plot(x[,1])

Daily time series simulation for the MSTL-algorithm

Description

This function simulates a daily time series according to the simulation model of Bandara, Hyndman and Bergmeir (2021) about the MSTL-algorithm for seasonal-trend decomposition. The simulated time series consists of a trend, weekly, annual and irregular component which are each simulated independently from each other. After the simulation process they are normalized and then combined to form the complete time series. As in the paper, this simulation function has the option to distinguish between a deterministic and a stochastic data generation process.

Usage

sim_daily_mstl(
  N,
  multiplicative = TRUE,
  start = 2020,
  sizeAnnualSeas = 100,
  sizeWeeklySeas = 100,
  sizeIrregularity = 100,
  shockAnnualSeas = 1,
  shockWeeklySeas = 1,
  deterministic = FALSE
)

Arguments

Value

Multiple simulated daily time series of class xts including:

original

The original series

seas_adj

The original series without seasonal effects

sfac7

The day-of-the-week effect

sfac365

The day-of-the-year effect

Author(s)

Nikolas Fritz, Daniel Ollech

References

Bandara, K., Hyndman, R. J., & Bergmeir, C. (2021). MSTL: A seasonal-trend decomposition algorithm for time series with multiple seasonal patterns. arXiv preprint arXiv:2107.13462.

Examples

x <- sim_daily_mstl(4)
ts.plot(x[,1])

Simulate a monthly seasonal series

Description

Simulate a monthly seasonal series

Usage

sim_monthly(
  N,
  sd = 5,
  change_sd = sd/10,
  beta_1 = 0.6,
  beta_tau = 0.4,
  moving = TRUE,
  model = list(order = c(3, 1, 1), ma = 0.5, ar = c(0.2, -0.4, 0.1)),
  start = c(2010, 1),
  multiplicative = TRUE,
  extra_smooth = FALSE
)

Arguments

Details

Standard deviation of the seasonal factor is in percent if a multiplicative time series model is assumed. Otherwise it is in unitless. Using a non-seasonal ARIMA model for the initialization of the seasonal factor does not impact the seasonality of the time series. It can just make it easier for human eyes to grasp the seasonal nature of the series. The definition of the ar and ma parameter needs to be inline with the chosen model.

Value

Multiple simulated monthly time series of class xts including:

original

The original series

seas_adj

The original series without seasonal effects

sfac

The seasonal effect

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Examples

x=sim_monthly(5, multiplicative=TRUE)
ts.plot(x[,1])

Simulate a monthly time series based on the HS model

Description

This function simulates a monthly time series with a Monte Carlo simulation based on an STS model based on Harvey and Shephard (1993) (HS model). The monthly data consists of a trend, annual seasonal and irregular component. The components are each simulated by a transition process with monthly random shocks and then combined at the end of the simulation to form the complete time series.

Usage

sim_monthly_hs(
  N,
  multiplicative = TRUE,
  sizeSeasonality = 100,
  sizeTrend = 100,
  sizeDrift = 100,
  sizeSeasonalityAux = 100,
  varIrregularity = 1,
  start = 2020,
  sizeBurnIn = 24,
  shockLevel = 1,
  shockDrift = 1,
  shockSeasonality = 1,
  index = 100
)

Arguments

Details

The impact of a component on the time series depends on its ratio to the other components. To increase (decrease) a component's impact, the value of the size needs to be increased (decreased) while the other components need to be kept constant. Therefore, the stability of the component (e.g. the shape of a seasonal component) also grows as the shocks on the given component have less impact. In order to increase the impact without increasing the stability, the variance of the shock also needs to be raised accordingly. The size of the components are defaulted to 100 each and the variances of the shocks are defaulted to 1.

The first effective year serves as base year for the time series

Value

Multiple simulated monthly time series of class xts including:

original

The original series

seas_adj

The original series without seasonal effects

sfac

The seasonal effect

Author(s)

Nikolas Fritz, Daniel Ollech, based on code provided by Ángel Cuevas and Enrique M Quilis

References

Cuevas, Ángel and Quilis, Enrique M., Seasonal Adjustment Methods for Daily Time Series. A Comparison by a Monte Carlo Experiment (December 20, 2023). Available at SSRN: https://ssrn.com/abstract=4670922 or http://dx.doi.org/10.2139/ssrn.4670922

Structural Time Series (STS) Monte Carlo simulation Z = trend + seasonal_weekly + seasonal_annual + irregular, according to Harvey and Shephard (1993): "Structural Time Series Models",in Maddala, G.S., Rao, C.R. and Vinod, H.D. (Eds.) Handbook of Statistics, vol. 11, Elsevier Science Publishers.

Examples

x <- sim_monthly_hs(4)
ts.plot(x[,1])

Monthly time series simulation for the MSTL-algorithm

Description

This function simulates a monthly time series according to the simulation model of Bandara, Hyndman and Bergmeir (2021) about the MSTL-algorithm for seasonal-trend decomposition. The simulated time series consists of a trend, annual seasonal and irregular component which are each simulated independently from each other. After the simulation process they are normalized and then combined to form the complete time series. As in the paper, this simulation function has the option to distinguish between a deterministic and a stochastic data generation process.

Usage

sim_monthly_mstl(
  N,
  multiplicative = TRUE,
  start = 2020,
  sizeSeasonality = 100,
  sizeIrregularity = 100,
  sizeTrend = 100,
  shockSeasonality = 1,
  deterministic = FALSE
)

Arguments

Value

Multiple simulated monthly time series of class xts including:

original

The original series

seas_adj

The original series without seasonal effects

sfac

The seasonal effect

Author(s)

Nikolas Fritz, Daniel Ollech

References

Bandara, K., Hyndman, R. J., & Bergmeir, C. (2021). MSTL: A seasonal-trend decomposition algorithm for time series with multiple seasonal patterns. arXiv preprint arXiv:2107.13462.

Examples

x <- sim_monthly_mstl(4)
ts.plot(x[,1])

Simulate an outlier

Description

Simulate an outlier

Usage

sim_outlier(
  n,
  k,
  freq = 12,
  type = c("AO", "LS", "TC"),
  effect_size = 10,
  start = c(2020, 1),
  multiplicative = TRUE
)

Arguments

Details

Three types of outliers are implemented: AO=Additive outlier, LS=Level shift, TC=Temporary Change. The effect size is stochastic as it is drawn from a normal distribution with mean equal to the specified effect_size and a standard deviation of 1/4*effect_size. This is multiplied randomly with -1 or 1 to get negative shocks as well. If multiplicative is true, the effect size is measured in percentage. If is not true, the effect size is unit less and thus adopts the unit of the time series the outliers are added to.

Value

The function returns k time series of class xts containing the k outlier effects

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Examples

plot(sim_outlier(60, 4, type=c("AO", "LS")))

Simulate a seasonal factor

Description

Simulate a seasonal factor

Usage

sim_sfac(
  n,
  freq = 12,
  sd = 1,
  change_sd = sd/10,
  moving = TRUE,
  beta_1 = 0.6,
  beta_tau = 0.4,
  start = c(2020, 1),
  multiplicative = TRUE,
  ar = NULL,
  ma = NULL,
  model = c(1, 1, 1),
  sc_model = list(order = c(1, 1, 1), ar = 0.65, ma = 0.25),
  smooth = TRUE,
  burnin = 7,
  extra_smooth = FALSE
)

Arguments

Details

Standard deviation of the seasonal factor is in percent if a multiplicative time series model is assumed. Otherwise it is in unitless. Using a non-seasonal ARIMA model does not impact the seasonality of the time series. It can just make it easier for human eyes to grasp the seasonal nature of the series. The definition of the ar and ma parameter needs to be in line with the chosen model.

Value

The function returns a time series of class ts containing a seasonal or periodic effect.

Author(s)

Daniel Ollech

References

Ollech, D. (2021). Seasonal adjustment of daily time series. Journal of Time Series Econometrics. doi:10.1515/jtse-2020-0028

Examples

ts.plot(sim_sfac(60))