{
  "_id": "6a102e84acfb0bcc41c944da",
  "Package": "MTS",
  "Type": "Package",
  "Title": "All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS)\nand Estimating Multivariate Volatility Models",
  "Version": "1.2.1",
  "Date": "2022-04-02",
  "Maintainer": "Ruey S. Tsay <ruey.tsay@chicagobooth.edu>",
  "Author": "Ruey S. Tsay [aut, cre], David Wood [aut], Jon Lachmann [ctb]",
  "Description": "Multivariate Time Series (MTS) is a general package for\nanalyzing multivariate linear time series and estimating\nmultivariate volatility models. It also handles factor models,\nconstrained factor models, asymptotic principal component\nanalysis commonly used in finance and econometrics, and\nprincipal volatility component analysis.  (a) For the\nmultivariate linear time series analysis, the package performs\nmodel specification, estimation, model checking, and prediction\nfor many widely used models, including vector AR models, vector\nMA models, vector ARMA models, seasonal vector ARMA models, VAR\nmodels with exogenous variables, multivariate regression models\nwith time series errors, augmented VAR models, and\nError-correction VAR models for co-integrated time series. For\nmodel specification, the package performs structural\nspecification to overcome the difficulties of identifiability\nof VARMA models. The methods used for structural specification\ninclude Kronecker indices and Scalar Component Models.  (b) For\nmultivariate volatility modeling, the MTS package handles\nseveral commonly used models, including multivariate\nexponentially weighted moving-average volatility, Cholesky\ndecomposition volatility models, dynamic conditional\ncorrelation (DCC) models, copula-based volatility models, and\nlow-dimensional BEKK models. The package also considers\nmultiple tests for conditional heteroscedasticity, including\nrank-based statistics.  (c) Finally, the MTS package also\nperforms forecasting using diffusion index , transfer function\nanalysis, Bayesian estimation of VAR models, and multivariate\ntime series analysis with missing values.Users can also use the\npackage to simulate VARMA models, to compute impulse response\nfunctions of a fitted VARMA model, and to calculate theoretical\ncross-covariance matrices of a given VARMA model.",
  "License": "Artistic License 2.0",
  "NeedsCompilation": "yes",
  "Packaged": {
    "Date": "2026-05-22 10:16:16 UTC",
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  "Repository": "https://rtsay1.r-universe.dev",
  "Date/Publication": "2022-04-11 13:32:30 UTC",
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    "author": "Ruey S. Tsay <ruey.tsay@chicagobooth.edu>",
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    "message": "version 1.2.1\n",
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  "_releases": [
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      "date": "2014-03-01"
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  "_exports": [
    "apca",
    "archTest",
    "backtest",
    "BEKK11",
    "Btfm2",
    "BVAR",
    "ccm",
    "comVol",
    "Corner",
    "dccFit",
    "dccPre",
    "diffM",
    "Eccm",
    "ECMvar",
    "ECMvar1",
    "EWMAvol",
    "FEVdec",
    "GrangerTest",
    "hfactor",
    "Kronfit",
    "Kronid",
    "Kronpred",
    "Kronspec",
    "MarchTest",
    "MCHdiag",
    "MCholV",
    "Mlm",
    "mq",
    "msqrt",
    "mtCopula",
    "MTSdiag",
    "MTSplot",
    "Mtxprod",
    "Mtxprod1",
    "PIwgt",
    "PSIwgt",
    "refECMvar",
    "refECMvar1",
    "refKronfit",
    "refREGts",
    "refSCMfit",
    "refsVARMA",
    "refVAR",
    "refVARMA",
    "refVARX",
    "refVMA",
    "refVMAe",
    "REGts",
    "REGtspred",
    "RLS",
    "SCCor",
    "SCMfit",
    "SCMid",
    "SCMid2",
    "SCMmod",
    "sVARMA",
    "sVARMACpp",
    "sVARMApred",
    "SWfore",
    "tfm",
    "tfm1",
    "tfm2",
    "VAR",
    "VARMA",
    "VARMAcov",
    "VARMACpp",
    "VARMAirf",
    "VARMApred",
    "VARMAsim",
    "VARorder",
    "VARorderI",
    "VARpred",
    "VARpsi",
    "VARs",
    "VARX",
    "VARXirf",
    "VARXorder",
    "VARXpred",
    "Vech",
    "VechM",
    "VMA",
    "VMACpp",
    "VMAe",
    "VMAorder",
    "VMAs",
    "Vmiss",
    "Vpmiss"
  ],
  "_datasets": [
    {
      "name": "ibmspko",
      "title": "Monthly simple returns of the stocks of International Business Machines (IBM) and Coca Cola (KO) and the S&P Composite index (SP)",
      "object": "mts-examples",
      "file": "mts-examples.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "date",
        "ibm",
        "sp",
        "ko"
      ],
      "rows": 612,
      "table": true,
      "tojson": true
    },
    {
      "name": "qgdp",
      "title": "Quarterly real gross domestic products of United Kingdom, Canada, and the United States",
      "object": "mts-examples",
      "file": "mts-examples.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "year",
        "mon",
        "uk",
        "ca",
        "us"
      ],
      "rows": 126,
      "table": true,
      "tojson": true
    },
    {
      "name": "tenstocks",
      "title": "Monthly simple returns of ten U.S. stocks",
      "object": "mts-examples",
      "file": "mts-examples.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "date",
        "TXN",
        "MU",
        "INTC",
        "TSM",
        "PFE",
        "MRK",
        "LLY",
        "JPM",
        "MS",
        "GS"
      ],
      "rows": 132,
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "MTS-package",
      "title": "Multivariate Time Series",
      "topics": [
        "MTS-package",
        "MTS"
      ]
    },
    {
      "page": "apca",
      "title": "Asymptotic Principal Component Analysis",
      "topics": [
        "apca"
      ]
    },
    {
      "page": "archTest",
      "title": "ARCH test for univariate time series",
      "topics": [
        "archTest"
      ]
    },
    {
      "page": "backtest",
      "title": "Backtesting of a scalar ARIMA model",
      "topics": [
        "backtest"
      ]
    },
    {
      "page": "BEKK11",
      "title": "BEKK Model",
      "topics": [
        "BEKK11"
      ]
    },
    {
      "page": "Btfm2",
      "title": "Back-Test of a Transfer Function Model with Two Input Variables",
      "topics": [
        "Btfm2"
      ]
    },
    {
      "page": "BVAR",
      "title": "Bayesian Vector Autoregression",
      "topics": [
        "BVAR"
      ]
    },
    {
      "page": "ccm",
      "title": "Cross-Correlation Matrices",
      "topics": [
        "ccm"
      ]
    },
    {
      "page": "comVol",
      "title": "Common Volatility",
      "topics": [
        "comVol"
      ]
    },
    {
      "page": "Corner",
      "title": "Compute the Corner table for transfer function model specification",
      "topics": [
        "Corner"
      ]
    },
    {
      "page": "dccFit",
      "title": "Dynamic Cross-Correlation Model Fitting",
      "topics": [
        "dccFit"
      ]
    },
    {
      "page": "dccPre",
      "title": "Preliminary Fitting of DCC Models",
      "topics": [
        "dccPre"
      ]
    },
    {
      "page": "diffM",
      "title": "Difference of multivariate time series",
      "topics": [
        "diffM"
      ]
    },
    {
      "page": "Eccm",
      "title": "Extended Cross-Correlation Matrices",
      "topics": [
        "Eccm"
      ]
    },
    {
      "page": "ECMvar",
      "title": "Error-Correction VAR Models",
      "topics": [
        "ECMvar"
      ]
    },
    {
      "page": "ECMvar1",
      "title": "Error-Correction VAR Model 1",
      "topics": [
        "ECMvar1"
      ]
    },
    {
      "page": "EWMAvol",
      "title": "Exponentially Weighted Moving-Average Volatility",
      "topics": [
        "EWMAvol"
      ]
    },
    {
      "page": "FEVdec",
      "title": "Forecast Error Variance Decomposition",
      "topics": [
        "FEVdec"
      ]
    },
    {
      "page": "GrangerTest",
      "title": "Granger Causality Test",
      "topics": [
        "GrangerTest"
      ]
    },
    {
      "page": "hfactor",
      "title": "Constrained Factor Model",
      "topics": [
        "hfactor"
      ]
    },
    {
      "page": "ibmspko",
      "title": "Monthly simple returns of the stocks of International Business Machines (IBM) and Coca Cola (KO) and the S&P Composite index (SP)",
      "topics": [
        "ibmspko"
      ]
    },
    {
      "page": "Kronfit",
      "title": "Fitting a VARMA Model via Kronecker Index",
      "topics": [
        "Kronfit"
      ]
    },
    {
      "page": "Kronid",
      "title": "Kronecker Index Identification",
      "topics": [
        "Kronid"
      ]
    },
    {
      "page": "Kronpred",
      "title": "Prediction of a fitted VARMA model via Kronfit, using Kronecker indices",
      "topics": [
        "Kronpred"
      ]
    },
    {
      "page": "Kronspec",
      "title": "Kronecler Index Specification",
      "topics": [
        "Kronspec"
      ]
    },
    {
      "page": "MarchTest",
      "title": "Multivariate ARCH test",
      "topics": [
        "MarchTest"
      ]
    },
    {
      "page": "MCHdiag",
      "title": "Multivariate Conditional Heteroscedastic Model Checking",
      "topics": [
        "MCHdiag"
      ]
    },
    {
      "page": "MCholV",
      "title": "Multivariate Cholesky Volatility Model",
      "topics": [
        "MCholV"
      ]
    },
    {
      "page": "Mlm",
      "title": "Multivariate Linear Model",
      "topics": [
        "Mlm"
      ]
    },
    {
      "page": "mq",
      "title": "Multivariate Ljung-Box Q Statistics",
      "topics": [
        "mq"
      ]
    },
    {
      "page": "msqrt",
      "title": "Square Root Matrix",
      "topics": [
        "msqrt"
      ]
    },
    {
      "page": "mtCopula",
      "title": "Multivariate t-Copula Volatility Model",
      "topics": [
        "mtCopula"
      ]
    },
    {
      "page": "MTS-internal",
      "title": "MTS Internal Functions",
      "topics": [
        "Lminv",
        "mFilter",
        "refVARs",
        "refVMAs",
        "revmq",
        "VARchi",
        "VARecm",
        "VARfore",
        "VARirf",
        "VMApred"
      ]
    },
    {
      "page": "MTSdiag",
      "title": "Multivariate Time Series Diagnostic Checking",
      "topics": [
        "MTSdiag"
      ]
    },
    {
      "page": "MTSplot",
      "title": "Multivariate Time Series Plot",
      "topics": [
        "MTSplot"
      ]
    },
    {
      "page": "Mtxprod",
      "title": "Polynomial Matrix Product",
      "topics": [
        "Mtxprod"
      ]
    },
    {
      "page": "Mtxprod1",
      "title": "Alternative Polynomial Matrix Product",
      "topics": [
        "Mtxprod1"
      ]
    },
    {
      "page": "PIwgt",
      "title": "Pi Weight Matrices",
      "topics": [
        "PIwgt"
      ]
    },
    {
      "page": "PSIwgt",
      "title": "Psi Wights Matrices",
      "topics": [
        "PSIwgt"
      ]
    },
    {
      "page": "qgdp",
      "title": "Quarterly real gross domestic products of United Kingdom, Canada, and the United States",
      "topics": [
        "qgdp"
      ]
    },
    {
      "page": "refECMvar",
      "title": "Refining Error-Correction Model for VAR series",
      "topics": [
        "refECMvar"
      ]
    },
    {
      "page": "refECMvar1",
      "title": "Refining ECM for a VAR process",
      "topics": [
        "refECMvar1"
      ]
    },
    {
      "page": "refKronfit",
      "title": "Refining VARMA Estimation via Kronecker Index Approach",
      "topics": [
        "refKronfit"
      ]
    },
    {
      "page": "refREGts",
      "title": "Refining a Regression Model with Time Series Errors",
      "topics": [
        "refREGts"
      ]
    },
    {
      "page": "refSCMfit",
      "title": "Refining Estimation of VARMA Model via SCM Approach",
      "topics": [
        "refSCMfit"
      ]
    },
    {
      "page": "refsVARMA",
      "title": "Refining a Seasonal VARMA Model",
      "topics": [
        "refsVARMA"
      ]
    },
    {
      "page": "refVAR",
      "title": "Refining a VAR Model",
      "topics": [
        "refVAR"
      ]
    },
    {
      "page": "refVARMA",
      "title": "Refining VARMA Estimation",
      "topics": [
        "refVARMA"
      ]
    },
    {
      "page": "refVARX",
      "title": "Refining a VARX Model",
      "topics": [
        "refVARX"
      ]
    },
    {
      "page": "refVMA",
      "title": "Refining VMA Models",
      "topics": [
        "refVMA"
      ]
    },
    {
      "page": "refVMAe",
      "title": "Refining VMA Estimation via the Exact Likelihood Method",
      "topics": [
        "refVMAe"
      ]
    },
    {
      "page": "REGts",
      "title": "Regression Model with Time Series Errors",
      "topics": [
        "REGts"
      ]
    },
    {
      "page": "REGtspred",
      "title": "Prediction of a fitted regression model with time series errors",
      "topics": [
        "REGtspred"
      ]
    },
    {
      "page": "RLS",
      "title": "Recursive Least Squares",
      "topics": [
        "RLS"
      ]
    },
    {
      "page": "SCCor",
      "title": "Sample Constrained Correlations",
      "topics": [
        "SCCor"
      ]
    },
    {
      "page": "SCMfit",
      "title": "Scalar Component Model Fitting",
      "topics": [
        "SCMfit"
      ]
    },
    {
      "page": "SCMid",
      "title": "Scalar Component Identification",
      "topics": [
        "SCMid"
      ]
    },
    {
      "page": "SCMid2",
      "title": "Scalar Component Model Specification II",
      "topics": [
        "SCMid2"
      ]
    },
    {
      "page": "SCMmod",
      "title": "Scalar Component Model specification",
      "topics": [
        "SCMmod"
      ]
    },
    {
      "page": "sVARMA",
      "title": "Seasonal VARMA Model Estimation",
      "topics": [
        "sVARMA"
      ]
    },
    {
      "page": "sVARMACpp",
      "title": "Seasonal VARMA Model Estimation (Cpp)",
      "topics": [
        "sVARMACpp"
      ]
    },
    {
      "page": "sVARMApred",
      "title": "Prediction of a fitted multiplicative seasonal VARMA model",
      "topics": [
        "sVARMApred"
      ]
    },
    {
      "page": "SWfore",
      "title": "Stock-Watson Diffusion Index Forecasts",
      "topics": [
        "SWfore"
      ]
    },
    {
      "page": "tenstocks",
      "title": "Monthly simple returns of ten U.S. stocks",
      "topics": [
        "tenstocks"
      ]
    },
    {
      "page": "tfm",
      "title": "Transfer Function Model",
      "topics": [
        "tfm"
      ]
    },
    {
      "page": "tfm1",
      "title": "Transfer Function Model with One Input",
      "topics": [
        "tfm1"
      ]
    },
    {
      "page": "tfm2",
      "title": "Transfer Function Model with Two Input Variables",
      "topics": [
        "tfm2"
      ]
    },
    {
      "page": "VAR",
      "title": "Vector Autoregressive Model",
      "topics": [
        "VAR"
      ]
    },
    {
      "page": "VARMA",
      "title": "Vector Autoregressive Moving-Average Models",
      "topics": [
        "VARMA"
      ]
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