The example analyzes yield curves derived from government bond data using the popular Diebold-Li yields-only model in the state-space model framework: Using the Kalman Filter to Estimate and Forecast the Diebold-Li Model.

The `fgls`

function
uses generalized least squares (GLS) to estimate coefficients and
standard errors in multiple linear regression models with nonspherical
errors by first estimating the covariance of the innovations process.

The example, following a series of time series regression examples, illustrates how to estimate multiple linear regression models of time series data in the presence of heteroscedastic or autocorrelated (nonspherical) innovations: Time Series Regression X: Generalized Least Squares and HAC Estimators.

Econometrics Toolbox has a model for performing univariate and multivariate time-series data analysis.

The

`ssm`

model supports time-invariant and time-varying, linear state-space models.Specify a state-space model using

`ssm`

, and then:

The methods of the state-space model, `ssm`

,
use the Kalman filter to estimate the states, and also use this framework
to manage missing data.

The following data set and example functions from the `matlab/toolbox/econ/econdemos`

folder
have moved to `matlab/toolbox/finance/findemos`

:

`Demo_AmericanBasket`

`Example_BarrierOption`

`Example_BlackScholes`

`Example_CEVModel`

`Example_CIRModel`

`Example_CopulaRNG`

`Example_LongstaffSchwartz`

`Example_StratifiedRNG`

`Data_GlobalIdx2.mat`

Function Name | What Happens When You Use This Function? | Use This Function Instead | Compatibility Considerations |
---|---|---|---|

`garchcount` | Errors | `sum(any(EstParamCov))` , where `EstParamCov` is
an estimated parameter covariance matrix of a fitted `arima` , `garch` , `egarch` ,
or `gjr` model | N/A |

`garchdisp` | Errors | `print` method
of the classes | Replace all existing instances of `garchdisp` with
the correct `print` syntax. |

`garchfit` | Errors | `estimate` method
of the classes `arima` , `garch` , `egarch` ,
or `gjr` | Replace all existing instances of `garchfit` with
the correct `estimate` syntax. |

`garchget` | Errors | `arima` , `garch` , `egarch` ,
or `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to retrieve parameter values from the model. |

`garchinfer` | Errors | `infer` method
of the classes `arima` , `garch` , `egarch` ,
or `gjr` | Replace all existing instances of `garchinfer` with
the correct `infer` syntax. |

`garchplot` | Errors | N/A | N/A |

`garchpred` | Errors | `forecast` method
of the classes `arima` , `garch` , `egarch` ,
or `gjr` | Replace all existing instances of `garchpred` with
the correct `forecast` syntax. |

`garchset` | Errors | `arima` , `garch` , `egarch` ,
or `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to set parameter values for the model. |

`garchsim` | Errors | `simulate` method
of the classes `arima` , `garch` , `egarch` ,
or `gjr` | Replace all existing instances of `garchsim` with
the correct `simulate` syntax. |

Econometrics Toolbox has a new model for performing time series regression analysis.

The

`regARIMA`

model supports linear regression models with ARIMA error processes, including AR, MA, ARMA, and seasonal error models.Specify a regression model with ARIMA errors using

`regARIMA`

, then

The example, following a series of time series regression examples, illustrates predictor history selection for multiple linear regression models: Time Series Regression IX: Lag Order Selection.

`optimoptions`

support `optimoptions`

support
when using solver optimization options to:

When estimating `arima`

, `garch`

, `egarch`

,
or `gjr`

models
using `estimate`

, the default solver options now
reference an `optimoptions`

object,
instead of an `optimset`

structure.
If you now use default solver options and operate on them assuming
this is an `optimset`

structure,
some operations might not work.

`optimoptions`

is
the default and recommended method to set solver options, though `optimset`

is
also supported.

The options for the Command Window display of `arima/estimate`

, `garch/estimate`

, `egarch/estimate`

,
and `gjr/estimate`

is
simplified and enhanced. You can easily:

Display only the maximum likelihood parameter estimates, standard errors, and

*t*statistics. This is the new default.Display only iterative optimization information.

Display only optimization diagnostics.

Display all of the above.

Turn off all output.

The new, recommended name-value pair argument that controls
the display is `Display`

. However, the software still
supports the previous name-value pair argument, `print`

.

Function Name | What Happens When You Use This Function? | Use This Function Instead | Compatibility Considerations |
---|---|---|---|

`garchcount` | Warns | Use `sum(any(EstParamCov))` , where `EstParamCov` is
an estimated parameter covariance matrix of a fitted `arima` , `garch` , `egarch` ,
or `gjr` model. | N/A |

`garchdisp` | Warns | `print` method
of the classes | Replace all existing instances of `garchdisp` with
the correct `print` syntax. |

`garchfit` | Warns | `estimate` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchfit` with
the correct `estimate` syntax. |

`garchget` | Warns | `arima` , `garch` , `egarch` ,
and `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to retrieve parameter values from the model. |

`garchinfer` | Warns | `infer` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchinfer` with
the correct `infer` syntax. |

`garchplot` | Warns | N/A | N/A |

`garchpred` | Warns | `forecast` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchpred` with
the correct `forecast` syntax. |

`garchset` | Warns | `arima` , `garch` , `egarch` ,
and `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to set parameter values for the model. |

`garchsim` | Warns | `simulate` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchsim` with
the correct `simulate` syntax. |

The new `hac`

function
estimates robust covariances for ordinary least squares coefficients
of multiple linear regression models under general forms of heteroscedasticity
and autocorrelation.

You can include a regression component to an `arima`

model
to measure the linear effects that exogenous covariate series have
on a response series. This new functionality also enhances `estimate`

, `filter`

, `forecast`

, `infer`

,
and `simulate`

.

This new `arima`

functionality replaces `garchfit`

, `garchdisp`

, `garchinfer`

, `garchget`

, `garchset`

, `garchpred`

,
and `garchsim`

. Change all instances of those functions
using the new `arima`

syntax.

Function Name | What Happens When You Use This Function? | Use This Function Instead | Compatibility Considerations |
---|---|---|---|

`garchcount` | Warns | Use `sum(any(EstParamCov))` , where `EstParamCov` is
an estimated parameter covariance matrix of a fitted `arima` , `garch` , `egarch` ,
or `gjr` model. | N/A |

`garchdisp` | Warns | `print` method
of the classes | Replace all existing instances of `garchdisp` with
the correct `print` syntax. |

`garchfit` | Warns | `estimate` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchfit` with
the correct `estimate` syntax. |

`garchget` | Warns | `arima` , `garch` , `egarch` ,
and `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to retrieve parameter values from the model. |

`garchinfer` | Warns | `infer` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchinfer` with
the correct `infer` syntax. |

`garchplot` | Warns | N/A | N/A |

`garchpred` | Warns | `forecast` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchpred` with
the correct `forecast` syntax. |

`garchset` | Warns | `arima` , `garch` , `egarch` ,
and `gjr` | Specify a model using the appropriate model creator `arima` , `garch` , `egarch` ,
or `gjr` . Use Dot
Notation to set parameter values for the model. |

`garchsim` | Warns | `simulate` method
of the classes `arima` , `garch` , `egarch` ,
and `gjr` | Replace all existing instances of `garchsim` with
the correct `simulate` syntax. |

There are new methods to filter user-specified disturbances through ARIMA and conditional variance models:

`filter`

for`arima`

model objects to filter disturbances through an ARIMA process.`filter`

for`garch`

model objects to filter disturbances through a GARCH process.`filter`

for`egarch`

model objects to filter disturbances through an EGARCH process.`filter`

for`gjr`

model objects to filter disturbances through a GJR process.

Eight new examples that illustrate common principles and tasks in time-series regression modeling:

Econometrics Toolbox has four new model objects for modeling univariate time series data.

Five new functions for each model object simplify the modeling
workflow: `estimate`

, `infer`

, `forecast`

, `print`

,
and `simulate`

.

Four new utility functions assist in time series analysis:

`corrplot`

plots predictor correlations.`collintest`

performs Belsley collinearity diagnostics.`i10test`

conducts paired integration and stationarity tests.`recessionplot`

adds recession bands to time series plots.

A new demo, "Specifying Static Time Series Models," steps through the model specification workflow for static multiple linear regression models.

Steps include:

Detecting multicollinearity

Identifying influential observations

Testing for spurious regression due to integrated data

Selecting predictor subsets using stepwise regression and

`lasso`

Conducting residual diagnostics

Forecasting

The demo uses many tools from Econometrics Toolbox, and introduces new utility functions useful for model specification.

To run the demo in the Command Window, use the command ```
showdemo
Demo_StaticModels
```

.

Econometrics Toolbox includes two new data sets:

**Data_CreditDefaults**. Historical data on investment-grade corporate bond defaults and four predictors, 1984–2004. Data are those used in: Loeffler, G., and P. N. Posch.*Credit Risk Modeling Using Excel and VBA.*West Sussex, England: Wiley Finance, 2007.**Data_Recessions**. U.S. recession start and end dates from 1857 to 2011. Source: National Bureau of Economic Research. "U.S. Business Cycle Expansions and Contractions."`http://www.nber.org/cycles.html`

.

Many warning and error IDs have changed from their previous versions. These warnings or errors typically appear during a function call.

If you use warning or error IDs, you might need to change the
strings you use. For example, if you turned off a warning for a certain
ID, the warning might now appear under a different ID. If you use
a `try/catch`

statement in your code, replace the
old identifier with the new identifier. There is no definitive list
of the differences, or of the IDs that changed.

Econometrics Toolbox now offers functions for cointegration
testing and modeling. The `egcitest`

function
uses Engle-Granger methods to test for individual cointegrating relationships,
and estimates their parameters. The `jcitest`

function
uses Johansen methods to test for multiple cointegrating relationships,
and estimates parameters in corresponding vector error-correction
models. The `jcontest`

function
tests linear restrictions on both error-correction speeds and the
space of cointegrating vectors, and estimates restricted model parameters.

Econometrics Toolbox includes three new data sets:

**Data_Canada**. Mackinnon's data on inflation and interest rates in Canada, 1954–1994. Data are those used in: MacKinnon, J. G. "Numerical Distribution Functions for Unit Root and Cointegration Tests."*Journal of Applied Econometrics*. v. 11, 1996, pp. 601–618.**Data_JDanish**,**Data_JAustralian**. Johansen's data on money and income in Denmark, 1974–1987, and Australia/U.S. purchasing power and interest parity, 1972–1991. Data are those used in: Johansen,*Likelihood-Based Inference in Cointegrated Vector Autoregressive Models*. Oxford: Oxford University Press, 1995.

Function Name | What Happens When You Use This Function? | Use This Function Instead | Compatibility Considerations |
---|---|---|---|

`dfARDTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfARDTest` with the correct `adftest` syntax. |

`dfARTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfARTest` with the correct `adftest` syntax. |

`dfTSTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfTSTest` with the correct `adftest` syntax. |

`ppARDTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppARDTest` with the correct `pptest` syntax. |

`ppARTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppARTest` with the correct `pptest` syntax. |

`ppTSTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppTSTest` with the correct `pptest` syntax. |

The economic data from the paper by Nielsen and Risager, "Stock
Returns and Bond Yields in Denmark, 1922–99," (Department
of Economics, Copenhagen Business School; Working paper 3-2001, 2001)
is now included with Econometrics Toolbox in the file `Data_Danish`

.

Function Name | What Happens When You Use This Function? | Use This Function Instead | Compatibility Considerations |
---|---|---|---|

`dfARDTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfARDTest` with the correct `adftest` syntax. |

`dfARTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfARTest` with the correct `adftest` syntax. |

`dfTSTest` | Error | `adftest` | The new function syntax differs. Replace all existing instances
of `dfTSTest` with the correct `adftest` syntax. |

`ppARDTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppARDTest` with the correct `pptest` syntax. |

`ppARTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppARTest` with the correct `pptest` syntax. |

`ppTSTest` | Error | `pptest` | The new function syntax differs. Replace all existing instances
of `ppTSTest` with the correct `pptest` syntax. |

A new demo, "Modeling the United States Economy," develops a small macroeconomic model. This model is used to examine the impact of various shocks on the United States economy, particularly around the period of the 2008 fiscal crisis. It uses the multiple time series tools from the Econometrics Toolbox.

To run the demo in the command window, use the command ```
echodemo
Demo_USEconModel
```

.

The new `LagOp`

polynomial
class provides methods to create and manipulate lag operator polynomials
and filter time series data, as well as methods to perform polynomial
algebra including addition, subtraction, multiplication, and division.

The new Leybourne-McCabe test function `lmctest`

assesses
the null hypothesis that a univariate time series *y* is
a trend-stationary `AR`

(*p*) process
against the alternative that *y* is a nonstationary `ARIMA`

(*p*,1,1)
process.

The new data set `Data_SchwertMacro`

contains
original data from G. William Schwert's article "Effects of
Model Specification on Tests for Unit Roots in Macroeconomic Data,"
(*Journal of Monetary Economics*, Vol. 20, 1987,
pp. 73–103.). These data are a benchmark for unit root tests.
The new data set `Data_SchwertStock`

contains indices
of U.S. stock prices as published in G. William Schwert's article
"Indexes of U.S. Stock Prices from 1802 to 1987," (*The
Journal of Business*,Vol. 63, 1990, pp. 399–42.).
The new data set `Data_USEconModel`

contains the macroeconomic
series for the new demo `Demo_USEconModel`

.

Econometrics Toolbox has a new set of naming conventions
for data sets. Data set names are prefixed by `Data_`

.

For full information on the available data sets, demos, and
examples, see Data
Sets, Demos, and Example Functions or type `help econ/econdemos`

at
the command line. For more information on Dataset Array objects, see `dataset`

in
the Statistics Toolbox™ documentation.

Replace any instances of `load Old_Data`

with `load`

and
the new file name.

All demos and examples in the Econometrics Toolbox have
been moved to the folder `econ/econdemos`

and renamed
according to the following convention:

Demos are named

`Demo_DemoName`

Examples are named

`Example_ExampleName`

Replace any instances of example functions with their new names.
For full information on the available, demos, and examples, see Data Sets, Demos,
and Example Functions or type `help econ/econdemos`

at
the command line.

There are now four classes of unit root tests. More information on the tests is available in the Unit Root Nonstationarity section of the User's Guide.

Dickey-Fuller and Phillips-Perron tests now have single interfaces,
with new capabilities for multiple testing. Both `adftest`

and `pptest`

test
a unit root null hypothesis against autoregressive, autoregressive
with drift, or trend-stationary alternatives.

The new `kpsstest`

function
tests a null hypothesis of (trend) stationarity against nonstationary
unit root alternatives.

The new `vratiotest`

function
tests a null hypothesis of a random walk against alternatives with
innovations that are not independent and identically distributed.

The `ardtest`

function replaces the `dfARDTest`

, `dfARTest`

,
and `dfTSTest`

functions. The `pptest`

function
replaces the `ppARDTest`

, `ppARTest`

,
and `ppTSTest`

functions. The new function syntax
differs from the functions they replace.

The Nelson and Plosser [50] data
set is now available. To access the data, enter `load Data_NelsonPlosser`

at
the MATLAB^{®} command line.

There are two new hypothesis tests for model misspecification:

Furthermore, the likelihood ratio test, `lratiotest`

,
has been enhanced to be able to "test up" as well as
"test down" when performing multiple model comparisons.
It now accepts vectors of model parameters for restricted log likelihoods,
for unrestricted log likelihoods, or for both.

There is a new demo about these tests; see New Demo.

`lratiotest`

error messages and message IDs
differ from previous versions.

Econometrics Toolbox multiple time series functions now include structural multiple time series. Structural models have the general form

$${A}_{0}{Y}_{t}=a+{X}_{t}b+{\displaystyle \sum _{i=1}^{p}{A}_{i}{Y}_{t-i}}+{\displaystyle \sum _{j=1}^{q}{B}_{j}{W}_{t-j}}+{B}_{0}{W}_{t}.$$

Previously, Econometrics Toolbox multiple time series functions addressed models of the form

$${Y}_{t}=a+{X}_{t}b+{\displaystyle \sum _{i=1}^{p}{A}_{i}{Y}_{t-i}}+{\displaystyle \sum _{j=1}^{q}{B}_{i}{W}_{t-j}}+{W}_{t}.$$

The mathematical difference is the inclusion of *A*_{0} and *B*_{0} matrices.
These matrices allow practitioners to specify structural dependencies
between variables. For more information, see the Multivariate Time
Series Models chapter of the Econometrics Toolbox User's
Guide.

Objects created with the Econometrics Toolbox V1.0 `vgxset`

function,
and saved in MAT files, do not work with Econometrics Toolbox V1.1
functions. Recreate the objects with the Econometrics Toolbox V1.1 `vgxset`

function.

A new suite of functions, listed in the following table, adds support for multivariate VAR, VARX, and VARMA models.

Function | Description |
---|---|

`vgxar` | Convert VARMA specification into a pure vector autoregressive (VAR) model |

`vgxcount` | Count restricted and unrestricted parameters in VAR or VARX models |

`vgxdisp` | Display VGX model parameters and standard errors in different formats |

`vgxget` | Get multivariate time-series specification parameters |

`vgxinfer` | Infer innovations of a VGX process |

`vgxloglik` | Compute conditional log-likelihoods of VGX process |

`vgxma` | Convert VARMA specification into a pure vector moving average (VMA) model |

`vgxplot` | Plot multivariate time series process |

`vgxpred` | Generate transient response of VGX process during a specified forecast period |

`vgxproc` | Generate a VGX process from an innovations process |

`vgxqual` | Determine if a VGX process is stable and invertible |

`vgxset` | Set or modify multivariate time-series specification parameters |

`vgxsim` | Simulate VGX processes |

`vgxvarx` | Solve VAR or VARX model using maximum likelihood estimation |

The new heston function adds support for Heston stochastic volatility models to the SDE engine.

The GARCH Toolbox™ software now allows you to model dependent financial and economic variables, such as interest rates and equity prices, via Monte Carlo simulation of multivariate diffusion processes. For more information, see Stochastic Differential Equations in the GARCH Toolbox documentation.

The `garchsim`

function previously allowed
you to specify the `State`

argument as either a scalar
or a time series matrix of standardized, independent, identically
distributed disturbances to drive the output `Innovations`

in
a time series process. The `State`

argument must
now be a time series matrix. See the `State`

input
argument on the `garchsim`

reference
page for more information.

No New Features or Changes

A new chapter in the *GARCH Toolbox User's Guide * explains
how to conduct Dickey-Fuller and Phillips-Perron unit root tests with
the new statistical functions in the toolbox.

Version 2.2 of the GARCH Toolbox software has six new functions. All of them support the ability to conduct univariate unit root tests on time series data. Three functions support augmented Dickey-Fuller unit root tests. The remaining three support Phillips-Perron unit root tests.

Function | Purpose |
---|---|

| Augmented Dickey-Fuller unit root test based on AR model with drift. |

| Augmented Dickey-Fuller unit root test based on zero drift AR model. |

| Augmented Dickey-Fuller unit root test based on trend stationary AR model. |

Function | Purpose |
---|---|

| Phillips-Perron unit root test based on AR(1) model with drift. |

| Phillips-Perron unit root test based on zero drift AR(1) model. |

| Phillips-Perron unit root test based on trend stationary AR(1) model. |

A change introduced in V2.1 of the GARCH Toolbox software
concerns user-specified noise processes. The `garchsim`

function
now allows you to provide a time series matrix of standardized, i.i.d.
disturbances to drive the output `Innovations`

in
a time series process. In previous versions, you could only provide
a state that was used to generate a random noise process. See the `State`

input
argument on the `garchsim`

reference
page for more information.

**garchsim argument Is renamed.** In
V2.1, the `garchsim`

argument `Seed`

is
renamed to `State`

for consistency with the MATLAB `rand`

and `randn`

functions.
The name change, in itself, introduces no backward incompatibilities.
The following topic explains a related change.

**garchsim defaults to current random number
generator state.** In V2.0.1 of the GARCH Toolbox software,
the `garchsim`

function
used the initial random number generator state, `0`

,
if you did not specify a value for the `Seed`

argument.
The `Seed`

argument corresponded to the `rand`

and `randn`

state
value.

In V2.1, if you do not specify a value for the `State`

(formerly `Seed`

)
argument, `garchsim`

uses
the current state of `rand`

and `randn`

,
rather than the initial state. Use the commands `s = rand('state')`

and ```
s
= randn('state')
```

to determine the current state of these
random number generators. For more information, see the `rand`

and `randn`

reference
pages.

Release | Features or Changes with Compatibility Considerations |
---|---|

R2015a | Functionality being removed |

R2014b | |

R2014a | |

R2013b | |

R2013a | |

R2012b | None |

R2012a | None |

R2011b | Warning and Error ID Changes |

R2011a | None |

R2010b | Functions Being Removed |

R2010a | |

R2009b | Unit Root Tests |

R2009a | |

R2008b | None |

R2008a | None |

R2007b | None |

R2007a | None |

R2006b | None |

R2006a | None |

R14SP3 | Changes to garchsim |

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