Package 'Rlgt' reference manual

Title:	Bayesian Exponential Smoothing Models with Trend Modifications
Description:	An implementation of a number of Global Trend models for time series forecasting that are Bayesian generalizations and extensions of some Exponential Smoothing models. The main differences/additions include 1) nonlinear global trend, 2) Student-t error distribution, and 3) a function for the error size, so heteroscedasticity. The methods are particularly useful for short time series. When tested on the well-known M3 dataset, they are able to outperform all classical time series algorithms. The models are fitted with MCMC using the 'rstan' package.
Authors:	Slawek Smyl [aut], Christoph Bergmeir [aut, cre], Erwin Wibowo [aut], To Wang Ng [aut], Xueying Long [aut], Alexander Dokumentov [aut], Daniel Schmidt [aut], Trustees of Columbia University [cph] (tools/make_cpp.R, R/stanmodels.R)
Maintainer:	Christoph Bergmeir <[email protected]>
License:	GPL-3
Version:	0.2-2
Built:	2024-10-15 06:57:47 UTC
Source:	CRAN

Getting started with the Rlgt package

Description

An implementation of Bayesian ETS models named LGT (for non-seasonal time series data) and SGT (for seasonal time series data). These models have been tested on the M3 competition dataset in which they outperform all of the models originally participating in the competition.

Getting started

The best way to get started with the package is to have a look at the vignettes and the various demos that ship with the package. There is a vignette with examples of how to use the various methods included in the package, and a vignette that discusses some of the theoretical background.

As to the demos, you can find their source code in the "demo" subfolder in the package sources (available on CRAN). There are some basic demos and other more advanced ones that run on subsets of the M3 dataset and run potentially for hours.

The package contains models for seasonal and non-seasonal data, allows for external regressors, and different error distributions. In the following, we briefly also present some of the theoretical background of the methods.

LGT (Local and Global Trend)

The LGT model is constructed based on Holt’s linear trend method. The model is designed to allow for a more general term of error by allowing for heteroscedasticity and an addition of constant "global" trend in the model.

Model Equations

In terms of mathematical notation, the model can be fully represented as follows:

$y_{t+1} \sim Student (\nu,y_{t+1}, \sigma _{t+1}) \quad (eq.1.1)$

$\widehat{y}_{t+1}=l_{t}+ \gamma l_{t}^{ \rho }+ \lambda b_{t} \quad (eq. 1.2)$

$l_{t+1}= \alpha y_{t+1}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 1.3)$

$b_{t+1}= \beta \left( l_{t+1}-l_{t} \right) + \left( 1- \beta \right) b_{t} \quad (eq. 1.4)$

$\widehat{\sigma}_{t+1}= \sigma l_{t}^{ \tau}+ \xi \quad (eq. 1.5)$

Notations

$y_{t}$: value of the dependent variable of interest at time t
$\widehat{y}_{t+1}$: forecasted value of y at time t+1 given information up to time t
$\widehat{\sigma}_{t+1}$: forecasted deviation at time t+1 given information up to time t
$l_{t}$: level at time t
$b_{t}$: local trend at time t

Parameters

$\nu$: degrees of freedom of the t-distribution
$\gamma$: coefficient of the global trend
$\rho$: power coefficient of the global trend
$\lambda$: damping coefficient of the local trend
$\alpha$: smoothing parameter for the level term
$\beta$: smoothing parameter for the local trend term
$\sigma$: coefficient of the size of error function
$\tau$: power coefficient of the size of error function
$\xi$: base or minimum value of the size of error function

SGT (Seasonal, Global Trend)

The SGT model was designed as a seasonal counterpart to the LGT model. Similar to LGT, this model is devised to allow for a global trend term and heteroscedastic error.

Model Equations

$y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 2.1)$

$\widehat{y}_{t+1}= \left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1} \quad (eq. 2.2)$

$l_{t+1}= \alpha \frac{y_{t+1}}{s_{t+1}}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 2.3)$

$s_{t+m+1}= \zeta \frac{y_{t+1}}{l_{t+1}}+ \left( 1- \zeta \right) s_{t+1} \quad (eq. 2.4)$

$\widehat{\sigma}_{t+1}= \sigma \widehat{y}_{t+1}^{ \tau}+ \xi \quad (eq. 2.5)$

Additional Notations

$s_{t}$: seasonality factor at time t
$m$: number of seasons in the data (e.g. 12 for monthly, 4 for quarterly)

Additional Parameters

$\zeta$: smoothing parameter for the seasonality terms

S2GT (Double Seasonal, Global Trend)

S2GT is designed as an extension to SGT for time series data which exhibit two seasonality patterns.

Model Equations

$y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 3.1)$

$\widehat{y}_{t+1}=\left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1}w_{t+1} \quad (eq. 3.2)$

$l_{t}= \alpha \frac{y_{t}}{s_{t}w_{t}}+ \left( 1- \alpha \right) \left( l_{t-1} \right) \quad (eq. 3.3)$

$s_{t+m}= \zeta \frac{y_{t}}{l_{t}w_{t}}+ \left( 1- \zeta \right) s_{t} \quad (eq. 3.4)$

$w_{t+d}= \delta \frac{y_{t}}{l_{t}s_{t}}+ \left( 1- \delta \right) w_{t} \quad (eq. 3.5)$

$\widehat{\sigma} _{t+1}= \sigma y_{t+1}^{ \tau}+ \xi \quad (eq. 3.6)$

Additional Notations

$w_{t}$: second seasonality factor prevailing at time t
$d$: number of (second) seasons in a complete period (e.g. 12 for monthly, 4 for quarterly)

Additional Parameters

$\delta$: smoothing parameters for the second seasonality factors

NA

Author(s)

Maintainer: Christoph Bergmeir [email protected]

Authors:

Slawek Smyl [email protected]
Erwin Wibowo [email protected]
To Wang Ng [email protected]
Xueying Long [email protected]
Alexander Dokumentov [email protected]
Daniel Schmidt [email protected]

Other contributors:

Trustees of Columbia University (tools/make_cpp.R, R/stanmodels.R) [copyright holder]

Rlgt LSGT Gibbs run in parallel

Description

Fit a list of series and produce forecast, then calculate the accuracy.

Usage

blgt.multi.forecast(
  train,
  future,
  n.samples = 20000,
  burnin = 10000,
  parallel = T,
  m = 1,
  homoscedastic = F
)
blgt.multi.forecast(
  train,
  future,
  n.samples = 20000,
  burnin = 10000,
  parallel = T,
  m = 1,
  homoscedastic = F
)

Arguments

`train`	A list of training series.
`future`	A list of corresponding future values of the series.
`n.samples`	The number of samples to sample from the posterior (the default is 2e4).
`burnin`	The number of burn in samples (the default is 1e4).
`parallel`	Whether run in parallel or not (Boolean value only, default `TRUE`).
`m`	The seasonality period, with default `m=1`, i.e., no seasonality specified.
`homoscedastic`	Run with homoscedastic or heteroscedastic version of the Gibbs sampler version. By default it is set to `FALSE`, i.e., run a heteroscedastic model.

Value

returns a forecast object compatible with the forecast package in R

Examples

## Not run: demo(exampleScript)
## Not run: 
## Build data and test
library(Mcomp)
M3.data <- subset(M3,"yearly")

train.data = list()
future.data = list()
for (i in 1:645)
{
  train.data[[i]] = as.numeric(M3.data[[i]]$x)
  future.data[[i]] = as.numeric(M3.data[[i]]$xx)  
}

## Test -- change below to test more series
w.series = 1:20
# w.series = 1:645        # uncomment to test all series

# use 10,000 posterior samples; change n.samples to 20,000 to test that as well if you want
s = system.time({
  rv=blgt.multi.forecast(train.data[w.series], future.data[w.series], n.samples=1e4)
})

s                         # overall timing info
s[[3]] / length(w.series) # per series time

mean(rv$sMAPE)            # performance in terms of mean sMAPE
mean(rv$InCI)/6           # coverage of prediction intervals -- should be close to 95%

## End(Not run)
## Not run: demo(exampleScript)
## Not run: 
## Build data and test
library(Mcomp)
M3.data <- subset(M3,"yearly")

train.data = list()
future.data = list()
for (i in 1:645)
{
  train.data[[i]] = as.numeric(M3.data[[i]]$x)
  future.data[[i]] = as.numeric(M3.data[[i]]$xx)  
}

## Test -- change below to test more series
w.series = 1:20
# w.series = 1:645        # uncomment to test all series

# use 10,000 posterior samples; change n.samples to 20,000 to test that as well if you want
s = system.time({
  rv=blgt.multi.forecast(train.data[w.series], future.data[w.series], n.samples=1e4)
})

s                         # overall timing info
s[[3]] / length(w.series) # per series time

mean(rv$sMAPE)            # performance in terms of mean sMAPE
mean(rv$InCI)/6           # coverage of prediction intervals -- should be close to 95%

## End(Not run)

Rlgt forecast

Description

produce forecasts from an rlgtfit object

Usage

## S3 method for class 'rlgtfit'
forecast(
  object,
  xreg = NULL,
  h = ifelse(frequency(object$x) > 1, 2 * frequency(object$x), 10),
  level = c(80, 95),
  NUM_OF_TRIALS = 2000,
  ...
)
## S3 method for class 'rlgtfit'
forecast(
  object,
  xreg = NULL,
  h = ifelse(frequency(object$x) > 1, 2 * frequency(object$x), 10),
  level = c(80, 95),
  NUM_OF_TRIALS = 2000,
  ...
)

Arguments

`object`	rlgtfit object
`xreg`	input regression matrix
`h`	forecasting horizon (the default is 10 for annual and 2*periods otherwise)
`level`	confidence levels for prediction intervals a.k.a. coverage percentiles. Musat be between 0 and 100.
`NUM_OF_TRIALS`	number of simulations to run. Suggested range is between (1000,5000), but it needs to be higher for good coverage for very high levels, e.g. 99.8.
`...`	currently not used

Value

returns a forecast object compatible with the forecast package in R

Examples

# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
print(rlgt_model)

# Produce Forecasts for the next 10 years
forecast_result <- forecast(rlgt_model, h = 10, level=c(80, 95, 98))

plot(forecast_result,main="Forecasting lynx dataset with LGT model")

# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
print(rlgt_model)

# Produce Forecasts for the next 10 years
forecast_result <- forecast(rlgt_model, h = 10, level=c(80, 95, 98))

plot(forecast_result,main="Forecasting lynx dataset with LGT model")

Weekly Initial Claims of US Unemployment Benefits & Google Trends Queries

Description

A dataset containing the weekly initial claims for US unemployment benefits against a few related Google trend queries from Jan 2010 - June 2018. This aims to mimick the dataset from Scott and Varian (2014).

Usage

data("iclaims.example")
data("iclaims.example")

Format

A data frame with 443 rows and 5 variables with log-transformation

week: date of records starting by Mondays with US calendar format
claims: weekly initial claims of unemployment benefits in thousands
trend.unemploy: normalized trend queries retreived from gtrendsR API
trend.filling: normalized trend queries retreived from gtrendsR API
trend.job: normalized trend queries retreived from gtrendsR API

References

U.S. Employment and Training Administration, Initial Claims [ICNSA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/ICNSA, October 27, 2018.

Trend queries from Google search engine. https://trends.google.com/trends/?geo=US

An interface for retrieving and displaying the information returned online by Google Trends is provided. Trends (number of hits) over the time as well as geographic representation of the results can be displayed. https://CRAN.R-project.org/package=gtrendsR

Scott, S. L. and Varian, H. R. (2014). Predicting the Present with Bayesian Structural Time Series. International Journal of Mathematical Modeling and Optimization 5 4–23.

Initialize a model from the Rlgt family

Description

This is an internal function that usually won't be called by users directly. It validates the model type and generates the corresponding list of parameters for the model.

Usage

initModel(
  model.type = NULL,
  use.regression = FALSE,
  seasonalityMethodId = 0,
  levelMethodId = 0,
  useSmoothingMethodForError = FALSE
)
initModel(
  model.type = NULL,
  use.regression = FALSE,
  seasonalityMethodId = 0,
  levelMethodId = 0,
  useSmoothingMethodForError = FALSE
)

Arguments

`model.type`	type of the forecasting model selected, a character object
`use.regression`	binary parameter indicating whether additional regressors will be used for forecasting in multivariate settings.
`seasonalityMethodId`	Seasonality method Id (0- HW, 1- generalized).
`levelMethodId`	Level method Id.
`useSmoothingMethodForError`	if the non-standard function for error size should be used, one based on smoothed innovations or surprises

Value

an Rlgt skeleton model

rlgtfit posterior interval

Description

This is a method of the link{rlgtfit} class to produce posterior intervals

Usage

## S3 method for class 'rlgtfit'
posterior_interval(object, prob = 0.9, type = "central", ...)
## S3 method for class 'rlgtfit'
posterior_interval(object, prob = 0.9, type = "central", ...)

Arguments

`object`	an object of class rlgtfit
`prob`	percentile level to be generated (multiple values can be accepted as a vector)
`type`	currently only central is available
`...`	currently not in use

Value

confidence interval

Examples

# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
posterior_interval(rlgt_model)
# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
posterior_interval(rlgt_model)

Generic print function for rlgtfit models

Description

Print out some characteristics of an rlgtfit model.

Usage

## S3 method for class 'rlgtfit'
print(x, ...)
## S3 method for class 'rlgtfit'
print(x, ...)

Arguments

`x`	an rlgtfit object
`...`	additional function parameters (currently not used)

Fit an Rlgt model

Description

The main function to fit an rlgt model. It fits the parameter values with MCMC.

Usage

rlgt(
  y,
  seasonality = 1,
  seasonality2 = 1,
  seasonality.type = c("multiplicative", "generalized"),
  error.size.method = c("std", "innov"),
  level.method = c("HW", "seasAvg", "HW_sAvg"),
  xreg = NULL,
  control = rlgt.control(),
  verbose = FALSE,
  method = "Stan",
  experimental = "",
  homoscedastic = F
)
rlgt(
  y,
  seasonality = 1,
  seasonality2 = 1,
  seasonality.type = c("multiplicative", "generalized"),
  error.size.method = c("std", "innov"),
  level.method = c("HW", "seasAvg", "HW_sAvg"),
  xreg = NULL,
  control = rlgt.control(),
  verbose = FALSE,
  method = "Stan",
  experimental = "",
  homoscedastic = F
)

Arguments

`y`	time-series data for training (provided as a numeric vector, or a ts, or msts object).
`seasonality`	This specification of seasonality will be overridden by frequency of y, if y is of ts or msts class. 1 by default, i.e. no seasonality.
`seasonality2`	Second seasonality. If larger than 1, a dual seasonality model will be used. However, this is experimental. If not specified and multiple seasonality time series (of msts class) is used, a single seasonality model will be applied, one with seasonality equal to the largest of seasonalities of the time series. 1 by default, i.e. no seasonality or single seasonality.
`seasonality.type`	Either "multiplicative" (default) or "generalized". The latter seasonality generalizes additive and multiplicative seasonality types.
`error.size.method`	Function providing size of the error. Either "std" (monotonically, but slower than proportionally, growing with the series values) or "innov" (proportional to a smoothed abs size of innovations, i.e. surprises)
`level.method`	"HW", "seasAvg", "HW_sAvg". Here, "HW" follows Holt-Winters approach. "seasAvg" calculates level as a smoothed average of the last seasonality number of points (or seasonality2 of them for the dual seasonality model), and HW_sAvg is an weighted average of HW and seasAvg methods.
`xreg`	Optionally, a vector or matrix of external regressors, which must have the same number of rows as y.
`control`	list of control parameters, e.g. hyperparameter values for the model's prior distributions, number of fitting interations etc.
`verbose`	whether verbose information should be printed (Boolean value only), default `FALSE`.
`method`	Sampling method, default `Stan`.
`experimental`	Run different versions ("nostudent", "noglobal", "nohet", "ets") for ablation studies
`homoscedastic`	Run with homoscedastic or heteroscedastic version of the Gibbs sampler version. By default it is set to `FALSE`, i.e., run a heteroscedastic model.

Value

rlgtfit object

Examples

# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
print(rlgt_model)

## Not run: demo(exampleScript)

# The following is a toy example that runs within a few seconds. To get good 
# fitting results the number of iterations should be set to at least 2000, and 
# 4 chains should be used (the default). To speed up computation the number of 
# cores should also be adjusted (default is 4).

rlgt_model <- rlgt(lynx, 
       control=rlgt.control(MAX_NUM_OF_REPEATS=1, NUM_OF_ITER=50, NUM_OF_CHAINS = 1, 
                            NUM_OF_CORES = 1), verbose=TRUE)

# print the model details
print(rlgt_model)

## Not run: demo(exampleScript)

Sets and initializes the control parameters

Description

This function initializes and sets the control parameters, i.e. hyperparameter values which control the prior distribution of the rlgtfit model. The purpose of this function is mainly to provide a default value for each of the hyperparameters. The function also accepts a customised set of values of the parameters as provided in the input of this function. This function is used in conjunction with the rlgt function.

Usage

rlgt.control(
  ADAPT_DELTA = 0.9,
  MAX_TREE_DEPTH = 12,
  NUM_OF_CHAINS = 4,
  NUM_OF_CORES = 4,
  ADD_JITTER = TRUE,
  CAUCHY_SD_DIV = 150,
  NUM_OF_ITER = 5000,
  MAX_NUM_OF_REPEATS = 2,
  MAX_RHAT_ALLOWED = 1.006,
  NUM_OF_SEASON_INIT_CYCLES = 3,
  MIN_NU = 2,
  MAX_NU = 20,
  MIN_POW_TREND = -0.5,
  MAX_POW_TREND = 1,
  POW_TREND_ALPHA = 1,
  POW_TREND_BETA = 1,
  POW_SEASON_ALPHA = 1,
  POW_SEASON_BETA = 1,
  MIN_SIGMA = 1e-10,
  MIN_VAL = 1e-30,
  MAX_VAL = 1e+38
)
rlgt.control(
  ADAPT_DELTA = 0.9,
  MAX_TREE_DEPTH = 12,
  NUM_OF_CHAINS = 4,
  NUM_OF_CORES = 4,
  ADD_JITTER = TRUE,
  CAUCHY_SD_DIV = 150,
  NUM_OF_ITER = 5000,
  MAX_NUM_OF_REPEATS = 2,
  MAX_RHAT_ALLOWED = 1.006,
  NUM_OF_SEASON_INIT_CYCLES = 3,
  MIN_NU = 2,
  MAX_NU = 20,
  MIN_POW_TREND = -0.5,
  MAX_POW_TREND = 1,
  POW_TREND_ALPHA = 1,
  POW_TREND_BETA = 1,
  POW_SEASON_ALPHA = 1,
  POW_SEASON_BETA = 1,
  MIN_SIGMA = 1e-10,
  MIN_VAL = 1e-30,
  MAX_VAL = 1e+38
)

Arguments

`ADAPT_DELTA`	Target Metropolis acceptance rate. See Stan manual. Suggested range is between (0.85-0.97).
`MAX_TREE_DEPTH`	NUTS maximum tree depth. See Stan manual for more details. Suggested range is between (10-15), defaut is 12.
`NUM_OF_CHAINS`	Number of MCMC chains. Suggested range is 3 to 4. Default is 4.
`NUM_OF_CORES`	Number of cores used for calculations. It can be smaller than NUM_OF_CHAINS, but for best computational speed, it should be equal to NUM_OF_CHAINS. Default is 4.
`ADD_JITTER`	Whether to add a very small amount (sd=min(y)*0.0001) of jitter to the input series. It is sometimes useful in cases of series with some perfectly flat sections. Default is TRUE.
`CAUCHY_SD_DIV`	Cauchy distribution is used for some parameters with non-obvious range. The error size hyperparameter of this distribution is calculated by dividing the max value of the time series by this constant. Suggested range is between (100,300). Default 150.
`NUM_OF_ITER`	Starting number of iterations for each chain. Suggested range is between (2000,10000). Default is 5000. Generally, the longer the series, the smaller is the value to reach convergence. Some models e.g. those with "innov" error size method are more difficult to fit and require more iterations.
`MAX_NUM_OF_REPEATS`	Maximum number of the sampling procedure repeats if the fit is unsatisfactorily, i.e. avgRHat>MAX_RHAT_ALLOWED. Each round will double the number of iterations which could potentially double the running time. Suggested range is between (2,4). Default is 2.
`MAX_RHAT_ALLOWED`	Maximum average value of Rhat's that suggests a good fit, i.e. the treshold below which the fit is considered as acceptable. Consult Stan's manual for more details on Rhat. Suggested range is between (1.005,1.02). Default is 1.006.
`NUM_OF_SEASON_INIT_CYCLES`	For seasonal models, number of seasonality periods used for establishing initial seasonality coefficients. Default is 3.
`MIN_NU`	Minimum degrees of freedom of the Student's distribution that is used in most models. Suggested range(1.2, 5). Default 2.
`MAX_NU`	Maximum degrees of freedom of the Student's distribution. Suggested range is between (15,30). Default 20.
`MIN_POW_TREND`	Minimum value of the global trend power coefficient. Suggested range is between (-1,0). Default -.5
`MAX_POW_TREND`	Maximum value of the global trend power coefficient. It should be 1 to allow the model to approach exponential growth when needed. Default is 1.
`POW_TREND_ALPHA`	Alpha parameter of Beta prior distribution. To make the forecast more upward curved, so to nudge it towards larger values, make the parameter larger. Suggested range is between (1,6) Default 1.
`POW_TREND_BETA`	Beta parameter of Beta prior distribution for the global trend power coefficient. 1 by default, see also above.
`POW_SEASON_ALPHA`	Alpha parameter of Beta distribution that is the prior of the power coefficient in the formula of the generalized seasonality in gSGT model. 1 by default, increasing it (say, to 3 or 5) will push the seasonality towards multiplicative behavior.
`POW_SEASON_BETA`	Beta parameter of Beta distribution that is the prior of the power coefficient in the formula of the generalized seasonality in gSGT model. 1 by default.
`MIN_SIGMA`	Minimum size of the fitted sigma, applied for numerical stability. Must be positive. 1e-10 by default.
`MIN_VAL`	Minimum value that forecast can take. Must be positive. 1e-30 by default.
`MAX_VAL`	Maximum value the forecast can take. 1e38 by default.

Value

list of control parameters

rlgtfit class

Description

A constructor function for objects of class rlgtfit, the main class of the package. Objects of this class are output from the rlgt function. This constructor will usually not be called by users directly.

Usage

rlgtfit(
  y,
  model.type,
  use.regression,
  seasonalityMethodId,
  levelMethodId,
  useSmoothingMethodForError = FALSE,
  seasonality,
  seasonality2,
  rlgtmodel,
  params,
  control,
  samples
)
rlgtfit(
  y,
  model.type,
  use.regression,
  seasonalityMethodId,
  levelMethodId,
  useSmoothingMethodForError = FALSE,
  seasonality,
  seasonality2,
  rlgtmodel,
  params,
  control,
  samples
)

Arguments

`y`	time series data for training (provided as a vector or a ts object).
`model.type`	the type of rlgt model, one of: "LGT", "SGT", "S2GT"
`use.regression`	whether the data has any additional variables to be used with forecasting, i.e. multivariate time-series.
`seasonalityMethodId`	Seasonality method Id (0- HW, 1- generalized).
`levelMethodId`	Level method Id.
`useSmoothingMethodForError`	if the non-standard function for error size should be used, one based on smoothed innovations or surprises
`seasonality`	This specification of seasonality will be overridden by frequency of y, if y is of ts or msts class. 1 by default, i.e. no seasonality.
`seasonality2`	Second seasonality. If larger than 1, a dual seasonality model will be used. This specification of seasonality will be overridden by the second seasonality of y, if y is of msts class. 1 by default, i.e. no seasonality or single seasonality.
`rlgtmodel`	an rlgt model.
`params`	list of parameters of the model (to be fitted).
`control`	list of control parameters, i.e. hyperparameter values for the model's prior distribution. See `rlgt.control`
`samples`	stanfit object representing the MCMC samples

Value

an rlgtfit instance

University of Michigan Monthly Survey of Consumer Sentiment & Google Trends Queries

Description

A dataset containing monthly University of Michigan survey of Consumer Sentiment along a few related google trend queries Jan from 2014 - June 2018. This aims to mimick the dataset from Scott and Varian (2014).

Usage

data("umcsent.example")
data("umcsent.example")

Format

A data frame with 174 rows and 8 variables with log-transformation

date: first date of each month in US calendar format
consumer.sent: monthly initial claims of University of Michigan: Consumer Sentiment
search.engine: normalized trend queries retreived from gtrendsR API
financial.planning: normalized trend queries retreived from gtrendsR API
bus.news: normalized trend queries retreived from gtrendsR API
investing: normalized trend queries retreived from gtrendsR API
energy.utilities: normalized trend queries retreived from gtrendsR API

References

University of Michigan, University of Michigan: Consumer Sentiment [UMCSENT], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/UMCSENT, November 17, 2018.

Trends queries from google search engine. https://trends.google.com/trends/?geo=US

Scott, S. L. and Varian, H. R. (2012). Bayesian Variable Selection for Nowcasting Economic Time Series. https://www.aeaweb.org/conference/2013/retrieve.php?pdfid=447

Package 'Rlgt'

Help Index

Getting started with the Rlgt package

Description

Getting started

LGT (Local and Global Trend)

Model Equations

Notations

Parameters

SGT (Seasonal, Global Trend)

Model Equations

Additional Notations

Additional Parameters

S2GT (Double Seasonal, Global Trend)

Model Equations

Additional Notations

Additional Parameters

NA

Author(s)

See Also

Rlgt LSGT Gibbs run in parallel

Description

Usage

Arguments

Value

Examples

Rlgt forecast

Description

Usage

Arguments

Value

Examples

Weekly Initial Claims of US Unemployment Benefits & Google Trends Queries

Description

Usage

Format

References

Initialize a model from the Rlgt family

Description

Usage

Arguments

Value

rlgtfit posterior interval

Description

Usage

Arguments

Value

Examples

Generic print function for rlgtfit models

Description

Usage

Arguments

Fit an Rlgt model

Description

Usage

Arguments

Value

Examples

Sets and initializes the control parameters

Description

Usage

Arguments

Value

rlgtfit class

Description

Usage

Arguments

Value

University of Michigan Monthly Survey of Consumer Sentiment & Google Trends Queries

Description

Usage

Format

References