Package 'micvar'

Simulate coefficient matrices with specified density

Description

Simulates coefficient matrices used to generate data from a vector autoregressive process.

Usage

gen_coef_mat(k, coefmin, coefmax, dens)

Arguments

k	Integer. Dimension of process.
coefmin	Numeric. Minimum value of coefficient. See Details.
coefmax	Numeric. Maximum value of coefficient. See Details.
dens	Numeric. Must be between 0 and 1. Specifies the proportion of non-zero entries in the coefficient matrix. The number of non-zero entries is computed as floor(k^2*dens).

Details

Coefficient values are drawn from a Uniform(coefmin, coefmax) or a Uniform(-coefmax, -coefmin) each with 50% probability.

Value

k x k matrix.

Examples

# bivariate coefficient matrix
coefmat <- gen_coef_mat(k = 2, coefmin = 0.1, coefmax = 0.3, dens = 0.8)
print(coefmat)

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Estimate order by mean square information criteria (MIC)

Description

Fits an autoregressive model to the data where the order is selected by minimizing the mean square information criteria. Model fitting is performed using ar. Any of the methods available in the method argument of ar can be used.

Usage

micvar(
  x,
  pmax,
  pmaxst = 2 * pmax,
  method = "ols",
  na.action = stats::na.fail,
  series = deparse1(substitute(x)),
  demean = TRUE,
  ...
)

Arguments

x	n x p time series data matrix. Can be univariate or multivariate time series. If x is not a matrix it will be coerced using as.matrix(x).
pmax	Integer. Maxmium number of lags to consider. Considered lags will to be 0,1,...,pmax.
pmaxst	Integer (default is 2pmax). Maximum lag used for computing self-tuned lambda. Must be larger than pmax.
method	Character string (default is "ols"). Specifies method to fit the model. Options are: c("ols", "burg", "mle", "yule-walker", "yw"). Note this function uses ar to perform model fitting.
na.action	Function for missing values (default is na.fail). See the na.action argument in ar.
series	Character string. Name of series. See the series argument in ar.
demean	Boolean (default is TRUE). Whether or not to demean the series. See the demean argument in ar.
...	Additional arguments for specific method. See ar and its various methods such as ar.yw and ar.ols and their corresponding arguments.

Details

This function uses the ar functions for fitting. For relevant details of those methods see the Details section of ar.

Value

List with elements. Many of these elements are similar to ar.

order	Order of fitted model selected by MIC
penalized_losses	Numeric vector of penalized losses for orders 0,1,...,pmax.
ar	Estimated autoregression coefficients. See the ar return value from ar.
var.pred	Prediction variance. See the var.pred return value from ar.
x.mean	Estimated mean. See the x.mean return value from ar.
x.intercept	Intercept. See the x.intercept return value from ar.
n.used	Number of observations in the time series including missing. See the n.used return value from ar.
n.obs	Number of non-missing observations. See the n.obs return value from ar.
pmax	The value of pmax argument.
partialacf	Estimate of partial autocorrelation. See the partialacf return value from ar.
resid	Residuals from fitted model. See the resid return value from ar.
method	Value of method argument.
series	Name of the series. See the series return value from ar.
call	Function call.
asy.var.coef	Asymptotic-theory variance matrix of coefficient estimates. See the asy.var.coef return value from ar.

Examples

# multivariate example - default is OLS
VAR3_2_A <- list(gen_coef_mat(3, 0.1, 0.3, 0.8), # lag 1
                 gen_coef_mat(3, 0.1, 0.4 , 0.5)) # lag 2
x <- sim_var(VAR3_2_A, n = 5000)
mic_model <- micvar(x, pmax = 10)

# burg and yule-walker examples
mic_model_burg <- micvar(x, pmax = 10, method = "burg")
mic_model_yw <- micvar(x, pmax = 10, method = "yw")

# univariate example
ar_coefs <- list(matrix(0.3,nrow=1), matrix(0.1,nrow=1))
x <- sim_var(ar_coefs, n = 5000)
mic_model <- micvar(x, pmax = 10)

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Simulate data from a vector autoregressive model with specified coefficient matrices

Description

Simulates data from a stable vector autoregressive model with Gaussian innovations and specified coefficient matrices. Stability of the process is verified using verify_stability.

Usage

sim_var(A, n, mu = NULL, Sigma = NULL, burn_in = 500)

Arguments

A	List of coefficient matrices. Each element in A must be a square matrix. Dimension of matrix determines the number of variables. Length of A determines the order of the process. In the case of univariate time series each entry of A should be a 1 x 1 matrix.
n	Integer. Number of data points to simulate.
mu	Vector (default 0s). Means of Gaussian innovations.
Sigma	Square matrix (default Identity). Variance of Gaussian innovations.
burn_in	Integer (default 500). Number of observations used to start up simulated process. In total n + burn_in observations are simulated but the first burn_in are discarded.

Value

n x k data matrix.

Examples

# multivariate
VAR3_2_A <- list(gen_coef_mat(3, 0.1, 0.3, 0.8), # lag 1
                 gen_coef_mat(3, 0.1, 0.4 , 0.5)) # lag 2
x <- sim_var(VAR3_2_A, n = 1000)

# univariate
AR2 <- list(matrix(0.5), matrix(0.2))
x <- sim_var(AR2, n = 1000)

# non-identity covariance of Gaussian innovations
Sigma <- matrix(c(1,0.5,0.9,0.5,1.5,0.7,0.9,0.7,1.25), nrow = 3)
x <- sim_var(VAR3_2_A, n = 1000, Sigma = Sigma)

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Verify stability of a vector autoregressive model

Description

Stability is verified using the method the method on pages 14-17 of (Lütkepohl 2005). Specifically we generate the coefficient matrix for the VAR(1) representation of the process and check that all eigenvalues have modulus less than 1.

Usage

verify_stability(A)

Arguments

A	List of coefficient matrices.

Value

None. Throws error if not stable process.

References

Lütkepohl H (2005). New introduction to multiple time series analysis. Springer Science & Business Media.

Examples

VAR3_2_A <- list(gen_coef_mat(3, 0.1, 0.3, 0.8), # lag 1
                 gen_coef_mat(3, 0.1, 0.4 , 0.5)) # lag 2
verify_stability(VAR3_2_A)

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