/usr/include/openturns/swig/ARMA_doc.i is in libopenturns-dev 1.7-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 | %feature("docstring") OT::ARMA
"ARMA process.
Available constructors:
ARMA()
ARMA(*ARCoeff, MACoeff, whiteNoise*)
ARMA(*ARCoeff, MACoeff, whiteNoise, ARMAstate*)
Parameters
----------
ARCoeff : :class:`~openturns.ARMACoefficients`
The coefficients of the AR part of the recurrence : :math:`(a_1, \\\\hdots, a_p)` in dimension 1 and :math:`(\\\\mat{A}_{\\\\, 1}, \\\\hdots, \\\\mat{A}{\\\\, _p})` in dimension :math:`d`.
Default is: :math:`0` in dimension 1 and the associated time grid is :math:`\\\\{0,1\\\\}`.
MACoeff : :class:`~openturns.ARMACoefficients`
The coefficients of the MA part of the recurrence : :math:`(b_1, \\\\hdots, b_q)` in dimension 1 and :math:`(\\\\mat{B}_{\\\\, 1}, \\\\hdots, \\\\mat{B}{\\\\, _p})` in dimension :math:`d`.
Default is: :math:`0` in dimension 1 and the associated time grid is :math:`\\\\{0,1\\\\}`.
whiteNoise : :class:`~openturns.WhiteNoise`
The white noise distribution of the recurrent relation.
Default is: the Normal distribution with zero mean and unit variance in dimension 1.
ARMAstate : :class:`~openturns.ARMAState`
The state of the ARMA process which will be extended to the next time stamps. The state is composed with :math:`p` values of the process and :math:`q` values of the white noise. This constructor is needed to get possible futurs from the current state.
Notes
-----
An ARMA process in dimension :math:`d` is defined by the linear recurrence :
.. math::
\\\\vect{X}_t + \\\\mat{A}_{\\\\, 1} \\\\, \\\\vect{X}_{t-1} + \\\\hdots + \\\\mat{A}_{\\\\, p} \\\\, \\\\vect{X}_{t-p} = \\\\vect{\\\\varepsilon}_{t}+ \\\\mat{B}_ {\\\\, 1} \\\\, \\\\vect{\\\\varepsilon}_{t-1}+ \\\\hdots + \\\\mat{B}_{\\\\, q} \\\\, \\\\vect{\\\\varepsilon}_{t-q}
where :math:`\\\\mat{A}_{\\\\, i} \\\\in \\\\Rset^d \\\\times \\\\Rset^d` and :math:`\\\\mat{B}_{\\\\, j} \\\\in \\\\Rset^d \\\\times \\\\Rset^d`.
In dimension 1, an ARMA process is defined by:
.. math::
X_t +a_1 X_{t-1} + \\\\hdots + a_p X_{t-p} = \\\\varepsilon_{t}+ b_1 \\\\varepsilon_{t-1}+ \\\\hdots +b_q \\\\varepsilon_{t-q}
where :math:`(a_i,b_i) \\\\in \\\\Rset`.
Examples
--------
Create an ARMA(4,2) process:
>>> import openturns as ot
>>> myTimeGrid = ot.RegularGrid(0.0, 0.1, 100)
>>> myWhiteNoise = ot.WhiteNoise(ot.Triangular(-1.0, 0.0, 1.0), myTimeGrid)
>>> myARCoef = ot.ARMACoefficients([0.4, 0.3, 0.2, 0.1])
>>> myMACoef = ot.ARMACoefficients([0.4, 0.3])
>>> myARMAProcess = ot.ARMA(myARCoef, myMACoef, myWhiteNoise)
>>> myLastValues = ot.NumericalSample([[0.6], [0.7], [0.3], [0.2]])
>>> myLastNoiseValues = ot.NumericalSample([[1.2], [1.8]])
>>> myARMAState = ot.ARMAState(myLastValues, myLastNoiseValues)
>>> myARMAProcessWithState = ot.ARMA(myARCoef, myMACoef, myWhiteNoise, myARMAState)
Generate a realization:
>>> myTimeSeries = myARMAProcess.getContinuousRealization()"
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getARCoefficients
"Accessor to the AR coefficients of the ARMA process.
Returns
-------
ARCoeff : :class:`~openturns.ARMACoefficients`
The AR coefficients of the linear recurrence defining the process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::setARCoefficients
"Accessor to the AR coefficients of the ARMA process.
Parameters
----------
ARCoeff : :class:`~openturns.ARMACoefficients`
The AR coefficients of the linear recurrence defining the process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getMACoefficients
"Accessor to the MA coefficients of the ARMA process.
Returns
-------
MACoeff : :class:`~openturns.ARMACoefficients`
The MA coefficients of the linear recurrence defining the process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::setMACoefficients
"Accessor to the MA coefficients of the ARMA process.
Parameters
----------
MACoeff : :class:`~openturns.ARMACoefficients`
The MA coefficients of the linear recurrence defining the process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getFuture
"Get possible futures from the current state of the ARMA process.
Parameters
----------
Nit : int, :math:`N_{it} \\\\geq 1`
The number of time stamps of the future.
Nreal : int, :math:`N_{real} \\\\geq 1`
The number of possible futures that are generated.
Default is: :math:`N_{real} = 1`.
Notes
-----
- If :math:`N_{real} = 1`:
A :class:`~openturns.TimeSeries`
One possible future of the ARMA process, from the current state over the next :math:`N_{it}` time stamps.
- If :math:`N_{real} > 1`:
A :class:`~openturnsProcessSample`
:math:`N_{real}` possible futures of the ARMA process, from the current state over the next :math:`N_{it}` time stamps.
Note that the time grid of each future begins at the last time stamp of the time grid associated to the time series which is extended."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getState
"Accessor to the stored state of the ARMA process.
Returns
-------
ARMAstate : :class:`~openturns.ARMAState`
The state of the ARMA process which will be extended to the next time stamps. The state is composed with :math:`p` values of the process and :math:`q` values of the white noise."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::setState
"Accessor to the stored state of the ARMA process.
Parameters
----------
ARMAstate : :class:`~openturns.ARMAState`
The state of the ARMA process which will be extended to the next time stamps. The state is composed with :math:`p` values of the process and :math:`q` values of the white noise."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getWhiteNoise
"Accessor to the white noise defining the ARMA process.
Returns
-------
whiteNoise : :class:`~openturns.WhiteNoise`
The white noise :math:`\\\\varepsilon` used in the linear recurrence of the ARMA process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::setWhiteNoise
"Accessor to the white noise defining the ARMA process.
Parameters
----------
whiteNoise : :class:`~openturns.WhiteNoise`
The white noise :math:`\\\\varepsilon` used in the linear recurrence of the ARMA process."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::computeNThermalization
"Accessor to the stored state of the ARMA process.
Parameters
----------
eps : float, :math:`\\\\epsilon > 0`
Returns
-------
Nther : int, :math:`N_{ther} \\\\geq 1`
The number of iterations of the ARMA process before being stationary and independent of its intial state.
Notes
-----
The thermalization number :math:`N_{ther}` is defined as follows:
.. math::
N_{ther} > E\\\\left[ \\\\displaystyle \\\\frac{\\\\ln \\\\epsilon}{\\\\ln \\\\max_{i,j} |r_{ij}|}\\\\right]
where :math:`E[]` is the integer part of a float and the :math:`(r_i)_i` are the roots of the polynomials (given here in dimension 1) :
.. math::
\\\\Phi(\\\\vect{r}) = \\\\vect{r}^p + \\\\sum_{i=1}^p a_i\\\\vect{r}^{p-i}
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::getNThermalization
"Accessor to the number of time stamps used to thermalize the process.
Returns
-------
Nther : int, :math:`N_{ther} \\\\geq 1`
The number of time stamps used to make the ARMA realization be independent from its actual state.
Default precision is: :math:`\\\\varepsilon = 2^{-53} \\\\equiv 10^{-16}`."
// ---------------------------------------------------------------------
%feature("docstring") OT::ARMA::setNThermalization
"Accessor to the number of time stamps used to thermalize the process.
Parameters
----------
Nther : int, :math:`N_{ther} \\\\geq 1`
The number of time stamps used to make the ARMA realization independent from its actual state."
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