computes the (sample) autocorrelation function for the time series x. The output vector starts with the autocorrelation r_0 at lag length 0 (and thus is equal to 1). The next entries are r_1, r_2 ... r_k.
plots the (sample) autocorrelation function of the time series x. The plot starts with the autocorrelation r_0 at lag length 0 (and is thus equal to 1).
calculates the test statistic 'tau' for a unit root in a time series according to the Augmented Dickey-Fuller test. Nonstandard critical values are given according to MacKinnon's response surface. t-values and corresponding probability-values are given for the coefficients of the lagged differences
This quantlet calculates either the Lagrange Multiplier (LM) form or the T-Rsquare (TR2) form of a test for conditional heteroskedasticity based on Artificial Neural Networks. The first argument of the function is the vector of residuals, the second optional argument is the order of the test, the t
calculates the neural network test for neglected nonlinearity proposed by Lee, White and Granger (1993). This statistic is evaluated from uncentered squared multiple correlation of an auxiliary regression in which the residuals are regressed on the original regressors and the principal components o
This quantlet calculates either the Lagrange Multiplier (LM) form or the R squared (TR2) form of Engle's ARCH test. The first argument of the function is the vector of residuals, the second optional argument is the lag order of the test. This ; second argument may be either a sca
estimates the ARIMA(1,d,1) process by Maximum Likelihood and computes diagnostics. Residuals diagnostics include their time plot with two-standard error bounds, correlograms and Ljung-Box statistics with p-values. Parameter diagnostics include their t-statistics with p-values and variance-covarianc
Estimation of ARIMA(p,d,q) models by conditional least squares, where residuals diagnostics and model selection criteria are given. Residuals diagnostics include their timeplot with two-standard error bounds, correlograms and the Ljung-Box statistic with p-values. Computed model selection criteria
Estimation of the ARI(p,d) process by OLS and diagnostics. Residuals diagnostics include their timeplot with two-standard error bounds, correlograms and Ljung-Box statistics with p-values. Parameter diagnostics include their t-statistics with p-values and variance-covariance matrix. Computed model
auxiliary quantlet that provides the analytical derivatives of the Gaussian log-likelihood of a bivariate BEKK-type volatility model with respect to its parameters
estimates the BEKK (Baba, Engle, Kraft, Kroner) volatility representation for a bivariate conditionally heteroscedastic time series and evaluates the maximum of the quasi log likelihood function in a GARCH(1,1) frame of the following form: S_t=C_(0)^T*C_(0)+A_(11)^T*e_(t-1)*e_(t-1)^T*A_(11)+G_(11)
computes the autocorrelation function (acf) and the Box-Ljung statistics for autocorrelation in a time series. Additionally, the p-values for the statistic are computed.
computes the autocorrelation function (acf) and the Box-Pierce statistics for autocorrelation in a time series. Additionally, the p-values for the statistic are computed.
Computes the correlation integral for time series. The instantaneous state of a dynamical system is characterized by a point in phase space. A sequence of such states subsequent in time defines the phase space trajectory. If the system is governed by deterministic laws, then after a while, it will
The EACF allows for the identification of ARIMA models (differencing is not necessary). The quantlet generates a table of the extended (sample) autocorrelation function (EACF) for the time series y. You have to specify the maximal number of AR lags (p) and MA lags (q). Every row of the output table
This quantlet calculates the empirical likelihood test statistic for the conditional expectation E[Y|X=x] of a time series (X,Y). X and Y are one-dimensional.
generates a time series e_t=u_t*s_t, where u_t is standard normal distributed and the variances s^2_t follow the GARCH process s^2_t = a_0 + a(B)e^2_t + b(B)s^2_t Here, B denotes the backshift (or lag) operator. You have to deliver the coefficient vectors a and b and the length T of t
generates an autoregressive moving average process (ARMA) in deviations from the mean form y_t = a(B)y_t + eps_t + b(B)eps_t B denotes the backshift (or lag) operator. You have to deliver the AR coefficients vector a, the MA coefficients vector b and the (T x 1) white noise series eps. Th
generates the bilinear process x that has the following form x_t = phi(B)x_t + e_t + theta(B)e_t + sum sum c_(i,j)x_(t-i)e_(t-j) B denotes the backshift (or lag) operator. The AR polynom phi(B) has p coefficients and the MA polynom theta(B) has q coefficients. The first sum of the double sum goes
generates the amplitude-dependent exponential AR (EXPAR) process x that has the following form x_t = a(B)x_t + exp{-delta x^2_(t-thrlag)}b(B)x_t + e_t B is the backshift (or lag) operator. The coefficient delta must be positive. The lag polynoms a(B) and b(B) must have the same order. e_t is a se
generates the threshold AR (TAR) process x that has the following form x_t = sum I{x_(t-thrlag) in (k_(i-1),k_i]}[phi_i(B)x_t]+e_t The sum goes from i=1 to nr (the number of threshold regions). I{} is an indicator function that takes the value 1 if the specified lagged value of x lies in the inte
Test procedure proposed by Hylleberg, Engle, Granger, Yoo (HEGY) for seasonal unit roots in quarterly time series. Deterministic components (constant, seasonal dummies and trend) can be included. The procedure renders a table with estimated coefficients and non-standard critical values given by HEG
detects jump points in the time series. Optional parameter alpha controls the the sensitivity of the procedure. Recomended values are 0.5 ... 4.0. The default value is 2.0. The output vector j, which has the same length as data, indicates the detected jumps. NaN values are not allowed.
Calculates estimates of mu, F, Q and R in a state-space model using EM-algorithm. The state-space model is assumed to be in the following form: y_t = H x_t + v_t x_t = F x_t-1 + w_t x_0 ~ (mu,Sig), v_t ~ (0,Q), w_t ~ (0,R)
Calculates observations of a given state-space model. The state-space model is assumed to be in the following form: y_t = H x_t + ErrY_t x_t = F x_t-1 + ErrX_t x_0 = mu
Calculates a filtered time series (uni- or multivariate) using the Kalman filter equations. The state-space model is assumed to be in the following form: y_t = H x_t + v_t x_t = F x_t-1 + w_t x_0 ~ (mu,Sig), v_t ~ (0,Q), w_t ~ (0,R) All parameters are assumed to be known.
Calculation of the KPSS statistics for I(0) against long-memory alternatives. We consider two tests, denoted by KPSS_mu and KPSS_t based on a regression on a constant mu, and on a constant and a time trend t, respectively. The quantlet returns the value of the estimated statistic for the two tests,
Calculates a smoothed time serie (uni- or multivariate) using the Kalman smoother equations. The state-space model is assumed to be in the following form: y_t = H x_t + v_t x_t = F x_t-1 + w_t x_0 ~ (mu,Sig), v_t ~ (0,Q), w_t ~ (0,R) All parameters are assumed known.
Semiparametric test for I(0) of a time series against fractional alternatives, i.e., long-memory and antipersistence. The test is semiparametric in the sense that it does not depend on a specific parametric form of the spectrum in the neighborhood of the zero frequency. The first argument of the fu
calculates the sum of squares of an ARMA(p,q) model and some diagnostics. Thereby, the model is conditioned on the first p observations of y and the first q residuals are set to 0.
used to specify a multiplicative seasonal ARIMA model. The arguments of the quantlet are three lists that give information about the difference orders, the ordinary ARMA part and the seasonal ARMA part.
Calculation of the Newey and West Heteroskedastic and Autocorrelation Consistent estimator of the variance. The first argument of the quantlet represents the series and the second optional argument the vector of truncation lags of the autocorrelation consistent variance estimator. If the second opt
fits a nonparametric GARCH(1,1) process e[t+1] = s[t+1]*Z[t+1], s[t+1]^2 = g(e[t]^2,s[t]^2), where Z[t] are iid Gaussian, by inverting deconvolution kernel estimators.
computes the (sample) partial autocorrelation function for the time series x. The output vector starts with the partial autocorrelation coefficient phi_1 at lag 1. The next entries are phi_2 ... phi_k.
Calculates the parzen window. Parzen windows classification is a technique for nonparametric density estimation, which can also be used for classification. In the Parzen window (Parzen, 1961), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:
Semiparametric average periodogram estimator of the degree of long memory of a time series. The first argument of the quantlet is the series, the second optional argument is a strictly positive constant q, which is also strictly less than one. The third optional argument is the bandwidth vector m.
Semiparametric Gaussian estimator of the degree of long memory of a time series, based on the Whittle estimator. The first argument is the series, the second argument is the vector of bandwidths, i.e., the number of frequencies after zero that are considered. By default, the bandwidth vector m = n/
Calculation of the rescaled variance test for I(0) against long-memory alternatives. The statistic is the centered kpss statistic based on the deviation from the mean. The limit distribution of this statistic is a Brownian bridge whose distribution is related to the distribution of the Kolmogorov s
Simulation of discrete observations of a Geometric Brownian Motion (GBM) via direct integration (method=1) or Euler scheme (method=2). The process follows the stochastic differential equation: dX(t) = mu X(t) dt + sigma X(t) dW(t).
Simulation of discrete observations of a generalized Ornstein-Uhlenbeck process via Euler scheme. The process follows the stochastic differential equation: dX(t) = beta (L - X(t)) dt + sigma (X(t)^gamma) dW(t).
generates real-life trajectory of the risk process from given data with premium corresponding to the non-homogeneous Poisson process and incorporating emprirical mean loss.
plots real-life trajectory of the risk process from given data with the premium corresponding to non-homogeneous Poisson process and incorporating given mean loss value.
Simulation of discrete observations of an Ornstein-Uhlenbeck process via its transition probability law. The simulated process follows the stochastic differential equation: dX(t) = aX(t) dt + s dW(t).
calculates the d'th difference of the time series x. Furthermore, it allows to calculate the s'th seasonal difference. In terms of the backshift (or lag) operator B, the series y_t = (1-B^s)^d x_t is generated. The default values are s=1 and d=1, which generate the first differences of the series x
Generates a display that shows the time series x in multiple windows with user-specified maximum length per window. It is possible to label the abscissa in a yearly format. However, you can not specify the periodicity of the labels (in that case, use timeplotlabel).
Generates a display that shows the time series x. The abscissa is labelled automatically, when the labels have the format year:1. One may specify the periodicity of the labels.