Package 'tvGarchKF'

Selective Stock Price Index

Description

The data covers the period from March 2000 to October 2014, totaling 3186 observations.

Usage

indipsa

Format

A time series object with 3186 elements

It's a stock market index that tracks the performance of a select group of Chilean companies.

Source

Yahoo Finance

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Generating Simulations using a tv-Garch Model

Description

Simulate from a tv-Garch(1,1) model.

Usage

tvGarch_Sim(
  n,
  gamma,
  alpha,
  beta,
  type = c("polynomial", "NoLineal", "trigonometric"),
  exponentes = NULL,
  trig = NULL,
  arg = NULL
)

Arguments

n	integer
gamma	Vector containing coefficents of c.
alpha	Vector containing coefficents of alpha.
beta	Vector containing coefficents of beta.
type	Vector of function type for c, alpha and beta.
exponentes	Vector for exponenets in NoLineal.
trig	Type of trigonometric function.
arg	Value of argument for the trigonometric function.

Value

An object of class 'zoo' with two components: the first component represents returns, while the second component denotes conditional variance.

Examples

## Simulate from a tv-GARCH(1,1) model lineal:
alpha_sim <- c(0.2, 0.2)
beta_sim <- c(0.45, 0.5, -0.85)
type_sim <- c("polynomial","polynomial","polynomial")
Sim1 <- tvGarch_Sim(n = 6000, gamma = 0.1, alpha = alpha_sim, beta = beta_sim, type = type_sim)
plot(Sim1[,1], type="l", main="Simulated tvGARCH(1, 1) process",
    ylim=c(-max(Sim1[,2]), max(Sim1[,2])))
lines(Sim1[,2], type="l", col="red")
legend("topright",legend=c("tvGARCH(1,1)",expression(sigma(u))),
      col=c("black","red"),lty=1,bty="n",lwd=1)
## Simulate from a tv-GARCH(1,1) model non linear:
alpha_sim2 <- c(0.75, 0.08)
beta_sim2 <- c(0.05, 0.03, 0.06)
type_sim2 <- c("polynomial","polynomial","NoLineal")
expo <- c(0, 1, 1/2)
Sim2<-tvGarch_Sim(n=6000,gamma=0.05,alpha=alpha_sim2,beta=beta_sim2,type=type_sim2,exponentes=expo)
plot(Sim2[,1], type="l", main="Simulated tvGARCH(1, 1) process",
     ylim=c(-max(Sim2[,2]),max(Sim2[,2])))
lines(Sim2[,2], type="l", col="red")
legend("topright",legend=c("tvGARCH(1,1)",expression(sigma(u))),
       col=c("black","red"),lty=1,bty="n",lwd=1)

---

Fit the time-varying (Tv) parameters of the GARCH model (tv-Garch) by using the Kalman Filter method. The tv-parameters are determined by deterministic functions of either linear or non-linear type.

Description

The tv-Garch(1,1) model, the parameters vary slowly over time according to linear or non-linear functions. These parameters are denoted by $c(t)$, $\alpha(t)$ and $\beta(t)$ which correspond to the model $\sigma_t = c(t) +\alpha(t) r^2_{t-1} +\beta(t)\sigma_{t-1}$.

Usage

tvGarchKalmanFit(
  series,
  c,
  alpha,
  beta,
  type = c("polynomial", "NoLineal", "trigonometric"),
  exponentes,
  trig,
  arg,
  predict = 0,
  trace.log = FALSE
)

Arguments

series	Time series.
c	Vector containing coefficents of c.
alpha	Vector containing coefficents of alpha.
beta	Vector containing coefficents of beta.
type	Vector of function type for c, alpha and beta.
exponentes	Vector for exponenets in NoLineal.
trig	Type of trigonometric function.
arg	Value of argument for the trigonometric function.
predict	Value for time to generate predict.
trace.log	Variable to print names of coefficients.

Details

The types of functions for the tv-parameters are: linear, non-linear, trigonometric, and exponential. For the case of the linear model, the tv-parameters follow the following structure:

$c(t) = c_0 + c_1u + c_2 u^2 + \ldots + c_p u^p,$

$\alpha(t) = a_0 + a_1u + a_2 u^2 + \ldots + a_p u^p,$

$\beta(t) = b_0 + b_1u + b_2 u^2 + \ldots + b_p u^p,$

where $u=t/T$, with $t=1, 2, \ldots, T$. For the non-linear case, it is as follows:

$c(t) = c_0 + \sum_{j=1}^k c_j u_{c,j},$

$\alpha(t) = a_0 + \sum_{j=1}^k a_j u_{\alpha,j},$

$\beta(t) = b_0 + \sum_{j=1}^k b_j u_{\beta,j},$

where $k$ it is positive value and $u_{c,j}$, $u_{\alpha,j}$ and $u_{\beta,j}$ are non linear function set. For the trigonometric case, it is as follows:

$c(t) = c_0 + c_1 g(u),$

$\alpha(t) = a_0 + a_1 g(u),$

$\beta(t) = b_0 + b_1 g(u),$

where $g(u)$ it is a trigonometric function, $cos$ or $sin$.

Value

Return fit values of omega, alpha and beta

Examples

ipsa<-diff(log(indipsa))
c <- c(0.05,0.05)
alpha <- c(0.05,0.05)
beta <- c(0.05,0.05)
type_fit <- c("trigonometric","trigonometric","trigonometric")
fit<-tvGarchKalmanFit(ipsa,c=c,alpha=alpha,beta=beta,type=type_fit,trig="cos",arg="3*(1-log(u))")

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Models tv-Garch Filter Kalman LogLikehood.

Description

It is the function to use in the process to fit coefficients.

Usage

tvGarchKalmanLoglike(
  x,
  series,
  c,
  alpha,
  beta,
  nsample = length(series),
  type = c("polynomial", "NoLineal", "trigonometric"),
  exponentes,
  trig,
  arg,
  predict,
  trace.log = FALSE
)

Arguments

x	Vector of coefficents to fit.
series	Time series.
c	Vector containing coefficents of c.
alpha	Vector containing coefficents of alpha.
beta	Vector containing coefficents of beta.
nsample	Value of time series length.
type	Vector of function type for c, alpha and beta.
exponentes	Vector for exponenets in NoLineal.
trig	Type of trigonometric function.
arg	Value of argument for the trigonometric function.
predict	Value for time to generate predict.
trace.log	Variable to print names of coefficients.

Value

Value of loglike in model.

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Models tv-Garch Filter Kalman print outputs.

Description

This function is designed to print the outputs of the tv-Garch model, which include the returns, conditional variance, log-likelihood value, and mean squared error (MSE).

Usage

tvGarchKalmanPrint(
  x,
  series,
  c,
  alpha,
  beta,
  nsample = length(series),
  type = c("polynomial", "NoLineal", "trigonometric"),
  exponentes,
  trig,
  arg,
  trace.log = FALSE,
  predict
)

Arguments

x	Vector of coefficents to fit.
series	Time series.
c	Vector containing coefficents of c.
alpha	Vector containing coefficents of alpha.
beta	Vector containing coefficents of beta.
nsample	Value of time series length.
type	Vector of function type for c, alpha and beta.
exponentes	Vector for exponenets in NoLineal.
trig	Type of trigonometric function.
arg	Value of argument for the trigonometric function.
trace.log	Variable to print names of coefficients.
predict	Value for time to generate predict.

Value

A data frame containing the following columns:

• X: State vector of Kalman equations.

• Fm: Value of MSE

• sigma: Conditional variance.

• loglike: Value of the loglike.

Examples

data(ipsa)
ipsa<-diff(log(indipsa))
c<-c(0.05,0.05)
alpha<-c(0.05,0.05)
beta<-c(0.05,0.05)
type_fit<-c("trigonometric","trigonometric","trigonometric")
fit<-tvGarchKalmanFit(ipsa,c=c,alpha=alpha,beta=beta,type=type_fit,trig="cos",arg="3*(1-log(u))")
arg_model<-"3*(1-log(u))"
model<-tvGarchKalmanPrint(fit,ipsa,c=c,alpha=alpha,beta=beta,type=type_fit,trig="cos",arg=arg_model)
plot(ipsa,ylab="",xlim=c(2000,2015))
lines(ts(model$sigma, star=2000, freq=225), col="red", lwd=2)
lines(ts(model$sigma*(-1), star=2000, freq=225), col="red", lwd=2)

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Structure of the Time-Varying GARCH(1,1) Parameters

Description

This function performs an exploratory analysis to uncover the dynamic structure of the time-varying GARCH(1,1) parameters. Specifically, the observation domain $\{1, \ldots,T\}$ is partitioned into $M$ overlapping blocks, each of length $N$, with a constant shift of size $S$ between consecutive blocks. The relation between these quantities satisfies $T = S(M-1)+N$. The midpoint of the $j$-th block, for $j=1,\ldots,M$, is denoted $t_j=S(j-1)+N/2$. For each block, a local estimation of the stationary GARCH(1,1) model is performed using the observations within that block. The resulting sequence of local estimates, evaluated across all blocks, provides an empirical trajectory that reflects the underlying evolution of the time-varying parameters. This trajectory can serve as a guide for selecting flexible function classes capable of capturing their temporal variation.

Usage

tvParameter(data, S, N, plot = TRUE)

Arguments

data	Represents the financial return series employed to investigate the temporal evolution of the parameters in the tv-GARCH(1,1) model.
S	The number of observations by which the analysis window is shifted to define the starting point of the next block; also known as the step size or shift parameter.
N	The total number of observations contained within each data block, representing the block or window length over which local model estimation is performed.
plot	A Boolean flag indicating whether a graphical representation of the estimation results should be generated.

Value

Data frame who contains omega, alpha, beta of GARCH(1,1) model and midpoint each block.

Examples

ipsa<-diff(log(indipsa))*100
S = 100
N = 800
tv <- tvParameter(ipsa,S,N)

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