急求matlab中predict函数的正确使用
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发布时间：2022-05-02 15:37
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时间：2022-06-17 15:50
predict
Predict output k steps ahead
Syntax
yp = predict(m,data)
[yp,x0p,mpred] = predict(m,data,k,'InitialState',init)
Description
data is the output-input data as an iddata object, and m is any idmodel or idnlmodel object. predict is meaningful only for time-domain data.
The argument k indicates that the k step-ahead prediction of y according to the model m is computed. In the calculation of yp(t), the model can use outputs up to time
t–k: y(s), s = t–k, t–k–1,...
and inputs up to the current time t. The default value of k is 1.
The output yp is an iddata object containing the predicted values as OutputData.
x0p is the used (estimated) initial state vector. For multiexperiment data, x0p is a matrix, whose columns contain the initial states for each experiment.
The output argument mpred contains the k step-ahead predictor. This is given as a cell array, whose kth entry is an idpoly model for the predictor of output number k. Note that these predictor models have as input both input and output signals in the data set. The channel names indicate how the predictor model and the data fit together.
init determines how to deal with the initial state:
init ='e(stimate)': The initial state is set to a value that minimizes the norm of the prediction error associated with the model and the data.
init = 'd(elayexpand)': Same as 'estimate', but for a model with nonzero InputDelay, the delays are first converted to explicit model delays (using inpd2nk) so that they are contained in x0p.
init = 'z(ero)' sets the initial state to zero.
init = 'm(odel)' uses the model's internally stored initial state.
init = x0, where x0 is a column vector of appropriate dimension, uses that value as initial state. For multiexperiment data, x0 can be a matrix whose columns give different initial states for each experiment. For a continuous-time model m, x0 is the initial state for this model. Any modifications of the initial state that sampling might require are automatically handled. If m has a non-zero InputDelay, and you need to access the values of the inputs ring this delay, you must first apply inpd2nk(m). When m is a continuous-time model, it must first be sampled before inpd2nk can be applied.
If init is not specified for linear models, its value is determined, as follows:
If m.InitialState is 'Estimate', 'Backcast', and 'Auto', init = 'Estimate'.
If m.InitialState is 'Zero', init = 'zero'.
If m.InitialState is 'Model' or 'Fixed', init = 'model'. For idss, idproc, and idgrey models, init corresponds to the m.x0 values. For other linear models, init = 'zero'.
If init is not specified for idnlgrey models, init = 'Model' is the default. The values and their estimation behavior are inherited from m.InitialStates.
If init is not specified for idnlarx models, init = 'Estimate' is the default. This corresponds to the first few samples of predicted outputs exactly matching the first few output samples in the data set.
If init is not specified for idnlhw models, init = 'Estimate' is the default. This computes initial states by minimizing the prediction errors over the available data range.
An important use of predict is to evaluate a model's properties in the mid-frequency range. Simulation with sim (which conceptually corresponds to k = inf) can lead to levels that drift apart, since the low-frequency behavior is emphasized. One step-ahead prediction is not a powerful test of the model's properties, since the high-frequency behavior is stressed. The trivial predictor can give good predictions in case the sampling of the data is fast.
Another important use of predict is to evaluate time-series models. The natural way of studying a time-series model's ability to reproce observations is to compare its k step-ahead predictions with actual data.
Note that for output-error models, there is no difference between the k step-ahead predictions and the simulated output, since, by definition, output-error models only use past inputs to predict future outputs.
Algorithms
The model is evaluated in state-space form, and the state equations are simulated k steps ahead with initial value , where is the Kalman filter state estimate.
Examples
Simulate a time series, estimate a model based on the first half of the data, and evaluate the four step-ahead predictions on the second half.
m0 = idpoly([1 -0.99],[],[1 -1 0.2]);
e = iddata([],randn(400,1));
y = sim(m0,e);
m = armax(y(1:200),[1 2]);
yp = predict(m,y,4);
plot(y(201:400),yp(201:400))
Note that the last two commands are also achieved by
compare(y,m,4,201:400);
See Also
compare | pe | sim | sims
clc, clear
a=[ ];
a=a'; a=a(:); a=a'; %把原始数据按照时间顺序展开成一个行向量
Rt=tiedrank(a) %求原始时间序列的秩
n=length(a); t=1:n;
Qs=1-6/(n*(n^2-1))*sum((t-Rt).^2) %计算Qs的值
t=Qs*sqrt(n-2)/sqrt(1-Qs^2) %计算T统计量的值
t_0=tinv(0.975,n-2) %计算上alpha/2分位数
b=diff(a) %求原始时间序列的一阶差分
m=ar(b,2,'ls') %利用最小二乘法估计模型的参数
bhat=predict(m,[b'; 0],1) %1步预测，样本数据必须为列向量,要预测1个值，b后要加1个任意数，1步预测数据使用到t-1步的数据
ahat=[a(1),a+bhat{1}'] %求原始数据的预测值，并计算t=15的预测值
delta=abs((ahat(1:end-1)-a)./a) %计算原始数据预测的相对误差追问一开始就看过了。。按他说的做结果有些问题。。。您能不能自己写个实际的程序呢
