Package 'tvCoef' reference manual

Title:	Linear Time-Varying Coefficient Models
Description:	Convert linear model to a time-varying coefficient model using stepwise regressions, local regressions or state-space models.
Authors:	Claire de Rosamel [aut], Alain Quartier-la-Tente [aut, cre]
Maintainer:	Alain Quartier-la-Tente <[email protected]>
License:	EUPL
Version:	0.2.1
Built:	2024-11-01 11:24:35 UTC
Source:	https://github.com/InseeFrLab/tvCoef

Pie regression

Description

Computes as many regressions as breakup dates within a global model

Usage

bp_lm(x, left = TRUE, break_dates, tvlm = FALSE, ...)
bp_lm(x, left = TRUE, break_dates, tvlm = FALSE, ...)

Arguments

`x`	`lm` object. It is the global regression model.
`left`	`logical`. By default set to `TRUE`, i.e. the breakdate is the end date of each submodel
`break_dates`	optional, to indicate the breakup dates if they are known.
`tvlm`	By default set to `FALSE`. Indicates which model will be run on each sub data. `FALSE` means a lm will be run.
`...`	other arguments passed to `tvReg::tvLM()`.

Value

Returns an element of class bp_lm. It is a list containing the following elements:

`model`	all computed models, each of class `lm` or `tvlm` according to the parameter specified above
`start`	start date of the time serie
`end`	end date of the time serie
`frequency`	frequency of the time serie
`breakdates`	a list of the breakup dates
`left`	same as the parameter specified above
`tvlm`	same as the parameter specified above

Break data

Description

Splits a database according to one (or more) date

Usage

break_data(x, break_dates, left = TRUE, names = NULL, ...)
break_data(x, break_dates, left = TRUE, names = NULL, ...)

Arguments

`x`	a `ts` or `mts` object to split
`break_dates`	the date(s) at which you want to divide the data
`left`	`logical`. By default set to `TRUE`, i.e. the breakdate is the end date of each subcolumn
`names`	optional vector containing the names of the variables used to build the splitted data. By default the function try to guess the names from the `x` parameter.
`...`	other unused arguments

Value

a mts containing as many times more data columns than breakdates

Extract Full Transformed Exogoneous matrix

Description

Extract Full Transformed Exogoneous matrix

Usage

full_exogeneous_matrix(model, ...)
full_exogeneous_matrix(model, ...)

Arguments

`model`	the model
`...`	other unused parameters

French GDP

Description

Dataset containing the quarterly growth of the total gross domestic product (GDP) of France and quarterly series of the French business climate in level and in difference.

Usage

gdp
gdp

Format

A quarterly ts object from 1949Q2 to 2024Q1.

Details

Dataset containing the quarterly growth of the total gross domestic product (GDP, "growth_gdp") of France, in volumes chained at previous year prices, seasonally and working day adjusted; and the French business climate in level.

The French business climate is a monthly series, it is transformed into three quarterly series using the month's place in the quarter. For example, "bc_fr_m1" contains the values in the first month of each quarter, and the "diff_fr_m1" is the difference of the previous variable (the 2000Q1 value corresponds to the difference in business climate between January 2000 and October 1999).

Data were downloaded March 15, 2024 and might therefore differ from the latest available data.

Source

INSEE

Get data function

Description

Retrieves the data used in the model

Usage

get_data(model, ...)

## S3 method for class 'lm'
get_data(model, start = 1, frequency = 1, ...)

## S3 method for class 'dynlm'
get_data(model, ...)

## S3 method for class 'tvlm'
get_data(model, end = numeric(), frequency = 1, ...)

## S3 method for class 'bp_lm'
get_data(model, ...)

## S3 method for class 'piece_reg'
get_data(model, ...)
get_data(model, ...)

## S3 method for class 'lm'
get_data(model, start = 1, frequency = 1, ...)

## S3 method for class 'dynlm'
get_data(model, ...)

## S3 method for class 'tvlm'
get_data(model, end = numeric(), frequency = 1, ...)

## S3 method for class 'bp_lm'
get_data(model, ...)

## S3 method for class 'piece_reg'
get_data(model, ...)

Arguments

`model`	the model
`...`	other unused parameters.
`start`	the start of the data.
`frequency`	the frequency of the data.
`end`	the end of the data.

Extract Formula From model

Description

Extract Formula From model

Usage

get_formula(x)

## Default S3 method:
get_formula(x)
get_formula(x)

## Default S3 method:
get_formula(x)

Arguments

`x`	the model.

Get elements of rmse_prev

Description

Get elements of rmse_prev

Usage

get_lm_coef(model)

get_tvlm_coef(model, date, variable)

get_tvlm_bw(model)

get_rmse_bw_small(model, ...)
get_lm_coef(model)

get_tvlm_coef(model, date, variable)

get_tvlm_bw(model)

get_rmse_bw_small(model, ...)

Arguments

`model`	result of rmse_prev fonction
`date`	the date on which we want the tvlm coefficients
`variable`	`integer`. The variable of which we want the coefficients at the given date
`...`	other unused parameters

Details

get_lm_coeff allows to get all coefficients of all linear regression prediction models

get_tvlm_coeff allows to get all coefficients of the variable at a certain date of all local regression prediction models

get_tvlm_bw allows to get the bandwidth of all local regression prediction models

get_rmse_bw_small allows to get rmse of linear, local and piecewise regression prediction models, when the bandwidth of the prediction model is different from 20.

get_coeff_plot plot get_tvlm_coeff of a certain variable at a certain date, get_lm_coeff of the same variable and the bandwidth of all prediction models, thanks to get_tvlm_bw. It also highlights when the bandwidth is equal to 20.

Hansen Table

Description

Hansen Table

Usage

hansen_table
hansen_table

Format

An object of class data.frame with 20 rows and 7 columns.

Source

Hansen, Bruce E. 1990. "Lagrange multiplier tests for parameter instability in non-linear models". University of Rochester. https://users.ssc.wisc.edu/~bhansen/papers/LMTests.pdf.

Hansen Test

Description

Performs Hansen test

Usage

hansen_test(x, var, sigma = FALSE)
hansen_test(x, var, sigma = FALSE)

Arguments

`x`	`lm` object.
`var`	variables used for the joint test. By default all the variable are used.
`sigma`	`logical` indicating if the joint test should include the variance

Details

Perform Hansen test, which indicates if the variance of a model, a global model and the coefficients of the variable within this model are likely to be unstable over time.

HO: the coefficient/model is stable over time.

References

Bruce E Hansen "Testing for parameter instability in linear models". Journal of policy Modeling (1992)

Examples

model_gdp <- lm(
formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
data = gdp
)
hansen_test(model_gdp)

model_gdp <- lm(
formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
data = gdp
)
hansen_test(model_gdp)

Check if model has intercept

Description

Check if model has intercept

Usage

has_intercept(x)
has_intercept(x)

Arguments

x

a model

Extract Last Coefficients

Description

Get last coefficients of lm or tvLM models.

Usage

last_coef(x)
last_coef(x)

Arguments

`x`	a 'tvlm' or 'lm' object

Fixed Window Regression

Description

Fixed Window Regression

Usage

lm_fenetre_fixe(formula, data, nbw = 1)
lm_fenetre_fixe(formula, data, nbw = 1)

Arguments

`formula`	a `formula` object.
`data`	time series data.
`nbw`	number of windows.

Value

Return an object of class "lmffixe". Return all models, from which we can extract the usual coefficients, residuals, and fitted.values. And the divisor chosen by the function (arbitrary the middle one), the period, i.e. the length of each sub models, and the frequency of the data.

Fixed and variable coefficients regressions

Description

Computes different types of regressions with some coefficients fixed and others allowed to vary

Usage

lm_fixed_coeff(formula, data, fixed_var, ...)
lm_fixed_coeff(formula, data, fixed_var, ...)

Arguments

`formula`	a `formula` object.
`data`	time series data.
`fixed_var`	chosen variables whose coefficients aren't allowed to vary through time
`...`	further arguments passed to `tvReg::tvLM()`

Value

`global_model`	the simple `lm` model
`linear_reg`	simple `lm` model with fixed coefficients
`piecewise_reg`	`bp_lm` model with fixed coefficients
`tv_reg`	`tvlm` model with fixed coefficients

Residual Effect Regression

Description

Checks there is no residual effect in a model

Usage

lm_residual_effect(x, var = c(-1))
lm_residual_effect(x, var = c(-1))

Arguments

`x`	`lm` object
`var`	the variables on which the residuals are to be regressed. By default use them all and cancel the explained variable

Examples

data("AirPassengers")
model <- lm(AirPassengers ~ time(AirPassengers))
lm_residual_effect(model)

data("AirPassengers")
model <- lm(AirPassengers ~ time(AirPassengers))
lm_residual_effect(model)

Business Surveys

Description

Dataset containing the quarterly growth of production in the manufacturing sector and its main sub-sectors, quarterly balance of opinion of business surveys published by INSEE and Banque de France and quarterly overhang of the industrial production index.

Usage

manufacturing
manufacturing

Format

A quarterly ts object from 1949Q2 to 2024Q1.

Details

Dataset containing the quarterly growth of production in the manufacturing sector and its main sub-sectors and quarterly series series of business surveys published by INSEE and Banque de France.

The sectors studied are:

Manufacturing industry
Food products and beverages (C1)
Capital goods (C3)
Transport equipments (C4)
Other manufacturing (C5)

"manuf_prod" contains the quarterly growth in production in the manufacturing sector, and the sub-sectors are in the form "prod_c1", "prod_c3", "prod_c4" and "prod_c5".

The overhang of the industrial production index corresponds to the quarterly growth obtained extending the series by the last known value:

"overhang_ipi0" is the quarterly growth obtained extending the series by the last value of the previous quarter (December, March, June, September);
"overhang_ipi1" is the quarterly growth obtained extending the series by the first value of the current quarter (January, April, July, October);
"overhang_ipi2" is the quarterly growth obtained extending the series by the second value of the current quarter (February, May, August, November).

The business surveys being monthly, the balance of opinion are transformed into three quarterly series using the month's place in the quarter (for example taking the values of January, April, July and October). Variable names are constructed as the combination of several codes defined as follows:

data source code (INSEE, ins, or Banque de France, bdf);

name of the balance of opinion:

Code	Definition
bc	Business climate
oscd	Overall order books
tppa and prodpas	Past production
tppre and prodpre	Personal production expectation
sitcar	Situation of order books
evocar	Evolution of order books
prix	Selling prices
stocks	Inventories of finished goods
tres	Cash position
tuc	Capacity utilisation rate

sector: nothing for the manufacturing industri and "c1", "c3", "c4" or "c5" for the sub-sectors;
place of the month in the quarter: m1, m2 or m3 for the first, second or third month of the quarter.

The dataset also contains some dummies labelled "indYYYYQX", where YYYY is the year and X is the quarter.

Source

INSEE, Banque de France

Detect Fixed or Moving Coefficients

Description

Functions to test if any coefficient is fixed or moving according to the Hansen test (hansen_test())

Usage

moving_coefficients(
  x,
  a = c(5, 1, 2.5, 7.5, 10, 20),
  sigma = FALSE,
  intercept = TRUE
)

fixed_coefficients(
  x,
  a = c(5, 1, 2.5, 7.5, 10, 20),
  sigma = FALSE,
  intercept = TRUE
)
moving_coefficients(
  x,
  a = c(5, 1, 2.5, 7.5, 10, 20),
  sigma = FALSE,
  intercept = TRUE
)

fixed_coefficients(
  x,
  a = c(5, 1, 2.5, 7.5, 10, 20),
  sigma = FALSE,
  intercept = TRUE
)

Arguments

`x`	`lm` object.
`a`	level
`sigma`	`logical` indicating if the joint test should include the variance
`intercept`	boolean indicating if the intercept should be consider as a moving coefficient when at least one other variable is moving.

Value

NULL if no variable selected, otherwise the order of the variables.

Out of sample forecast (or simulated out of sample)

Description

Out of sample forecast (or simulated out of sample)

Usage

oos_prev(model, date = 28, period = 1, ...)

## S3 method for class 'lm'
oos_prev(model, date = 28, period = 1, data = NULL, ...)

## S3 method for class 'piece_reg'
oos_prev(model, date = 28, period = 1, ...)

## S3 method for class 'tvlm'
oos_prev(
  model,
  date = 28,
  period = 1,
  data_est = NULL,
  fixed_bw = FALSE,
  bw = NULL,
  end = numeric(),
  frequency = 1,
  ...
)

## S3 method for class 'bp_lm'
oos_prev(
  model,
  date = 28,
  period = 1,
  data_est = NULL,
  data,
  fixed_bw = FALSE,
  bw = NULL,
  ...
)

## S3 method for class 'piece_reg'
oos_prev(model, date = 28, period = 1, ...)
oos_prev(model, date = 28, period = 1, ...)

## S3 method for class 'lm'
oos_prev(model, date = 28, period = 1, data = NULL, ...)

## S3 method for class 'piece_reg'
oos_prev(model, date = 28, period = 1, ...)

## S3 method for class 'tvlm'
oos_prev(
  model,
  date = 28,
  period = 1,
  data_est = NULL,
  fixed_bw = FALSE,
  bw = NULL,
  end = numeric(),
  frequency = 1,
  ...
)

## S3 method for class 'bp_lm'
oos_prev(
  model,
  date = 28,
  period = 1,
  data_est = NULL,
  data,
  fixed_bw = FALSE,
  bw = NULL,
  ...
)

## S3 method for class 'piece_reg'
oos_prev(model, date = 28, period = 1, ...)

Arguments

`model`	an object used to select a method
`date`	choose when we want to start the revision process after the start date. By default set to 28 periods.
`period`	choose by how many values we want to move forward. By default set to 1.
`...`	other arguments
`data`	a `ts` object containing the variables in the model. Necessary only when `x` is a formula.
`data_est`, `end`, `frequency`	optional arguments to specify the data used to estimate the model, the last date and the frequency
`fixed_bw`	`logical`, by default set to `FALSE`. Indicates if the bandwidth has to be computed again in the forecast model, or if it takes the value of the bandwidth of the `tvlm` model.
`bw`	bandwidth of the local regression (when `tvlm = TRUE`).

Value

oos_prev returns an object of class revision, only for models of class lm and tvlm. For an object of class bplm it returns the same forecasts and residuals as below. An object of class revision is a list containing the following elements:

`model`	all models used to forecast
`debut`	same as date chosen earlier
`intervalle`	same as period chosen earlier
`end_dates`	a vector of all end date of each models
`frequency`	the frequency of the data
`forecast`	the forecast
`residuals`	the errors of the forecast

Examples

data_gdp <- window(gdp, start = 1980, end = c(2019, 4))
reg_lin <- lm(
  formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
  data = data_gdp
)
oos <- oos_prev(reg_lin)
data_gdp <- window(gdp, start = 1980, end = c(2019, 4))
reg_lin <- lm(
  formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
  data = data_gdp
)
oos <- oos_prev(reg_lin)

Piecewise regression

Description

Computes one global linear regression, on splitted data

Usage

piece_reg(
  x,
  break_dates = NULL,
  fixed_var = NULL,
  tvlm = FALSE,
  bw = NULL,
  left = TRUE,
  ...
)
piece_reg(
  x,
  break_dates = NULL,
  fixed_var = NULL,
  tvlm = FALSE,
  bw = NULL,
  left = TRUE,
  ...
)

Arguments

`x`	`lm` object. It is the global regression model
`break_dates`	optional, to indicate the breakdates if they are known. By default set to `NULL`.
`fixed_var`	fixed variables (not splitted using `break_dates`).
`tvlm`	By default set to `FALSE`. Indicates which model will be run on each sub data. `FALSE` means a lm will be run.
`bw`	bandwidth of the local regression (when `tvlm = TRUE`).
`left`	`logical`. By default set to `TRUE`, i.e. the breakdate is the end date of each submodel
`...`	other arguments passed to `tvReg::tvLM()`.

Details

Computes possible breakdates if not filled in. Uses function break_data and run a linear regression on the same splitted data.

Value

Returns an element of class lm

Extract data frame for lm_fixed_coeff

Description

According to parameter fixed_var, computes a new explained variable, which is the explained variable minus the product between estimated coefficients and values of the fixed variables.

Usage

resid_lm_fixed(x, fixed_var)
resid_lm_fixed(x, fixed_var)

Arguments

`x`	`lm` model
`fixed_var`	list of variables that don't vary through time according to hansen_test

Value

A new environment where the explained variable is named "fixed".

Root mean squarred error

Description

Root mean squarred error

Usage

rmse(resid)
rmse(resid)

Arguments

resid

the residuals vector on which rmse will be calculated

Computes RMSE of different models

Description

Computes 6 models: linear regression, piecewise regression (with linear regression and local regression), local regression (with tvLM), piecewise regression with some fixed coefficients and tvlm with fixed coefficients. Computes 6 rmse on their residuals and 6 others on the residuals of the predictions of these models.

Usage

rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)

## S3 method for class 'formula'
rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)

## S3 method for class 'lm'
rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)
rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)

## S3 method for class 'formula'
rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)

## S3 method for class 'lm'
rmse_prev(x, data, fixed_var = NULL, fixed_bw = FALSE, ...)

Arguments

`x`	an object of class `formula` or `lm`, that is the description of the model to be fitted, or the model itself.
`data`	a `ts` object containing the variables in the model. Necessary only when `x` is a formula.
`fixed_var`	which variables of the model should have their coefficients fixed for the models with fixed coefficients. Obtained thanks to the hansen test.
`fixed_bw`	`logical`, by default set to `FALSE`. Indicates if the bandwidth has to be computed again in the forecast model, or if it takes the value of the bandwidth of the `tvlm` model.
`...`	additional arguments

Details

In additional arguments, parameters as date and period can be informed. As in oos_prev they are by default respectively set to 28 and 1.

To estimate forecast models, the function oos_prev is used.

For the forecasts of the two models with fixed coefficients, fixed coefficients are re-estimated at each date, before bp_lm or tvLM are run on moving variables.

Value

Returns an object of class prev which is a list containing the following elements:

`model`	a list of the 6 explanatory models
`forecast`	a list of the 6 predictions of the 6 previous models
`rmse`	a list of the 2 computed rmse, in sample and out of sample

State space model

Description

Computes state space model with one equation. Starting with a simple lm model, build the all state space model and run it.

Use rjd3sts packages.

Usage

ssm_lm(
  x,
  trend = FALSE,
  var_intercept = 0,
  var_slope = 0,
  var_variables = 0,
  fixed_var_intercept = TRUE,
  fixed_var_trend = TRUE,
  fixed_var_variables = TRUE,
  ...,
  remove_last_dummies = FALSE,
  intercept = TRUE
)
ssm_lm(
  x,
  trend = FALSE,
  var_intercept = 0,
  var_slope = 0,
  var_variables = 0,
  fixed_var_intercept = TRUE,
  fixed_var_trend = TRUE,
  fixed_var_variables = TRUE,
  ...,
  remove_last_dummies = FALSE,
  intercept = TRUE
)

Arguments

`x`	a `lm` or `dynlm` model
`trend`	boolean indicating if the model should have a trend.
`var_intercept`, `var_slope`	variance of the intercept (used if `ìntercept = TRUE`) and the slope (used if `trend = TRUE`).
`var_variables`	variance of the other variables: can be either a single value (same variance for all the variables) or a vector specifying each variance.
`fixed_var_intercept`, `fixed_var_trend`, `fixed_var_variables`	logical indicating if the variance are fixed or estimated.
`...`	other arguments used in `rjd3sts::estimate()`.
`remove_last_dummies`	boolean indicating if current dummies (i.e.: only 0 and 1 at the last date) should be removed.
`intercept`	boolean indicating if the model should have an intercept.

Value

Returns a list containing:

`smoothed_states`	$E[a_t\|y_0,\dots,y_n]$
`smoothed_stdev`	$\sqrt{V[a_t\|y_0,\dots,y_n]}$
`filtering_states`	$E[a_t\|y_0,\dots,y_{t-1}]$
`filtering_stdev`	$\sqrt{V[a_t\|y_0,\dots,y_{t-1}]}$
`parameters`	some estimation parameters
`data`	data used in the original model

Examples

data_gdp <- window(gdp, start = 1980, end = c(2019, 4))
reg_lin <- lm(
  formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
  data = data_gdp
)
ssm <- ssm_lm(reg_lin, fixed_var_intercept = FALSE, fixed_var_variables = FALSE)
ssm
summary(ssm)
data_gdp <- window(gdp, start = 1980, end = c(2019, 4))
reg_lin <- lm(
  formula = growth_gdp ~ bc_fr_m1 + diff_bc_fr_m1,
  data = data_gdp
)
ssm <- ssm_lm(reg_lin, fixed_var_intercept = FALSE, fixed_var_variables = FALSE)
ssm
summary(ssm)

Out of sample forecast of state space model

Description

Computes out of sample forecasts of a given state space model. Unlike ssm_lm it can manage dummies.

Usage

ssm_lm_oos(
  x,
  trend = FALSE,
  var_intercept = 0,
  var_slope = 0,
  var_variables = 0,
  fixed_var_intercept = TRUE,
  fixed_var_trend = TRUE,
  fixed_var_variables = TRUE,
  date = 28,
  ...
)
ssm_lm_oos(
  x,
  trend = FALSE,
  var_intercept = 0,
  var_slope = 0,
  var_variables = 0,
  fixed_var_intercept = TRUE,
  fixed_var_trend = TRUE,
  fixed_var_variables = TRUE,
  date = 28,
  ...
)

Arguments

`x`	a `lm` or `dynlm` model
`trend`	boolean indicating if the model should have a trend.
`var_intercept`, `var_slope`	variance of the intercept (used if `ìntercept = TRUE`) and the slope (used if `trend = TRUE`).
`var_variables`	variance of the other variables: can be either a single value (same variance for all the variables) or a vector specifying each variance.
`fixed_var_intercept`, `fixed_var_trend`, `fixed_var_variables`	logical indicating if the variance are fixed or estimated.
`date`	choose when we want to start the revision process after the start date. By default set to 28 periods.
`...`	other arguments used in `rjd3sts::estimate()`.

Value

Returns all coefficients of all variables and the residual

Package 'tvCoef'

Help Index

Pie regression

Description

Usage

Arguments

Value

Break data

Description

Usage

Arguments

Value

Extract Full Transformed Exogoneous matrix

Description

Usage

Arguments

French GDP

Description

Usage

Format

Details

Source

Get data function

Description

Usage

Arguments

Extract Formula From model

Description

Usage

Arguments

Get elements of rmse_prev

Description

Usage

Arguments

Details

Hansen Table

Description

Usage

Format

Source

Hansen Test

Description

Usage

Arguments

Details

References

Examples

Check if model has intercept

Description

Usage

Arguments

Extract Last Coefficients

Description

Usage

Arguments

Fixed Window Regression

Description

Usage

Arguments

Value

Fixed and variable coefficients regressions

Description

Usage

Arguments

Value

Residual Effect Regression

Description

Usage

Arguments

Examples

Business Surveys

Description

Usage

Format

Details

Source

Detect Fixed or Moving Coefficients

Description

Usage

Arguments