pear: fit a periodic autoregression model

Description Usage Arguments Details Value Side Effects References See Also Examples

Description

Periodic time series models of any order, say m[j], for the j-th period, j=1,...,p can be fit to a periodic time series of period p. A generalization of the Yule-Walker method is used so that when p=1 the results from this function will be equivalent to the Splus function ar.yw(). If desired the aic or bic criterion can be used to select the model orders. Otherwise the user can select based on the partial autocorrelation function as suggested in Box and Jenkins (1976) and McLeod (1994).

Usage

1
pear(z, m, ic="none")

Arguments

z

a univariate time series object. Note that the period of z is given by attr(z, "tsp")[3]. Additional information about the time series can be provided in a title string by setting attr(z, "title") to the desired string. This title will then be displayed on the plot. Abbreviations for the periods may be provided in attr(z, "abb"). For example, to use the standard monthly abbreviations: attr(z, "abb")<-month.abb. These abbreviations will be used to aid one in interpreting the output.

m

If ic="none" then m is a required argument. In this case m specifies the order of the periodic autoregression to be fitted. Typically m is specified as a vector of length p where p is the period and m[k], k=1,...,p indicates the order for the k-th period. For convenience, if all periods are the same order then m can just be that scalar value. When ic="aic" or ic="bic" then the argument m is ignored.

ic

The default ic="none" means the model orders are supplied. Otherwise if ic="aic" or ic="bic" the automatic criteria aic or bic are used.

Details

Let z[t] be a period time series with period p and let m[j] denote the order of the autoregressive model for the j-th period, j=1,...,p. The parameters of this model can be estimated using the Yule-Walker type equations given in McLeod eq (3.1) and (3.2). The covariance matrix of the autoregressive parameters is obtained by replacing the theoretical autocovariances in eq (3.3, note addendum correction) with their sample values.

Value

a list with the following named components: model.orders vector of length p, indicating the fitted ar order for each period k, k=1,...,p phi matrix of dimension p by m where m = max(model.orders). The (i,j) entry is phi[i,j] which is the autoregression coefficient for period i and lag j. se.phi matrix of standard deviations for the estimated phi's. For those phi's set to 0, the corresponding se.phi's are also set to 0. resvar vector of length p residuals time series object of length(z) portmanteau.test list: portmanteau test at various lags The named components of this list are: QM = matrix of portmanteau statistics for each period and lag QM.df = corresponding df of QM QM.sl = corresponding sl of QM residual.acf residual autocorrelation matrix residual.acf.sd estimated standard errors of the residual autocorrelations cov list with p components: cov[[i]] is the estimated covariance matrix for the parameters of period i

Side Effects

none

References

Hipel, K.W. and McLeod, A.I. (1994) "Time Series Modelling of Water Resources and Environmental Systems" Elsevier, Amsterdam ISBN 0-444-89270-2. (1013 pages).

McLeod, A.I. (1994), "Diagnostic Checking of Periodic Autoregression" Journal of Time Series Analysis, Vol. 15, No. 2, pp.221–233.

McLeod, A.I. (1995), Errata (see file errata.tex included with these files)

See Also

peacf, pepacf, ar.yw

Examples

1
2
data(Fraser)
pear(log(Fraser), ic="bic")

Example output

$model.orders
 period 1  period 2  period 3  period 4  period 5  period 6  period 7  period 8 
        1         1         1         1         1         3         2         1 
 period 9 period 10 period 11 period 12 
        1         3         1         1 

$phi
              lag 1      lag 2     lag 3
period 1  0.6633120  0.0000000 0.0000000
period 2  0.7616731  0.0000000 0.0000000
period 3  0.8127845  0.0000000 0.0000000
period 4  0.7652456  0.0000000 0.0000000
period 5  0.2018468  0.0000000 0.0000000
period 6  0.2609638 -0.2603229 0.1984197
period 7  0.7691441 -0.1708642 0.0000000
period 8  0.7508529  0.0000000 0.0000000
period 9  0.7505846  0.0000000 0.0000000
period 10 1.1590270 -0.6816364 0.3640488
period 11 0.7543983  0.0000000 0.0000000
period 12 0.7451919  0.0000000 0.0000000

$se.phi
               lag 1      lag 2      lag 3
period 1  0.06411463 0.00000000 0.00000000
period 2  0.06830949 0.00000000 0.00000000
period 3  0.07801672 0.00000000 0.00000000
period 4  0.12172331 0.00000000 0.00000000
period 5  0.06715109 0.00000000 0.00000000
period 6  0.07954896 0.05963304 0.07706646
period 7  0.10493248 0.08051855 0.00000000
period 8  0.06854167 0.00000000 0.00000000
period 9  0.08905648 0.00000000 0.00000000
period 10 0.13656207 0.20895763 0.16588797
period 11 0.09123781 0.00000000 0.00000000
period 12 0.07113319 0.00000000 0.00000000

$resvar
  period 1   period 2   period 3   period 4   period 5   period 6   period 7 
0.02947049 0.02544491 0.03173720 0.08818641 0.04713156 0.02345282 0.02533583 
  period 8   period 9  period 10  period 11  period 12 
0.01581397 0.02495953 0.03599596 0.05159159 0.03847035 

$residuals
               Jan           Feb           Mar           Apr           May
1912                              0.000000e+00  5.721555e-02  1.175709e-01
1913 -3.258406e-01  2.596907e-01 -2.226714e-01 -2.222533e-01 -4.688577e-01
1914  4.067548e-01 -1.784681e-01  1.570446e-01  1.811963e-01  1.343034e-01
1915 -1.744470e-02 -9.860352e-02  8.031318e-02  4.490414e-01 -2.267148e-01
1916 -1.003728e-01  5.067634e-01 -1.414051e-01 -1.992890e-01 -1.556473e-01
1917 -8.176069e-02 -1.092491e-01 -1.724108e-01 -3.430667e-01  1.980510e-02
1918  3.538601e-01 -1.567799e-01 -8.208499e-02  9.487146e-02  6.224578e-02
1919 -1.308004e-01 -1.323231e-01 -2.009289e-01  2.062348e-01 -1.250024e-01
1920  6.614437e-02 -9.087964e-02 -2.252497e-01 -4.585874e-01 -4.922424e-02
1921 -3.350202e-02  4.293999e-02 -4.596902e-02 -3.071827e-02  1.193670e-01
1922 -1.458264e-01 -2.183531e-01 -1.495018e-01 -3.973890e-01 -3.460873e-02
1923 -4.821564e-02 -2.211147e-01 -1.092823e-01  8.305990e-02  4.383948e-02
1924 -2.769485e-01  4.168267e-01 -1.950578e-01 -5.142389e-01  3.606164e-01
1925 -1.230843e-01 -4.329207e-02 -9.079959e-02  4.364792e-01  3.309091e-01
1926  1.778208e-02 -2.199408e-01  1.235637e-01  4.088300e-01 -9.218828e-02
1927 -1.596624e-03 -1.766224e-01 -1.241188e-01 -3.199559e-01 -2.395240e-01
1928  1.838263e-01 -1.861212e-01  5.125989e-02 -3.677473e-02  3.170613e-01
1929 -9.055998e-02 -1.028659e-01 -5.384942e-02 -5.050318e-01 -3.710180e-01
1930  2.831683e-01 -1.068893e-01 -2.106693e-01  3.045650e-01 -3.257996e-01
1931  1.152278e-02 -4.857992e-02  5.291106e-02 -3.028069e-01 -3.057653e-02
1932 -8.086112e-02  8.860597e-02  2.041928e-01  1.665643e-01  8.595320e-02
1933 -9.829030e-02 -1.757170e-01 -1.024656e-01 -1.123653e-01  1.205825e-01
1934  9.888489e-02  1.844503e-01  2.834700e-02  4.108331e-01  1.658607e-01
1935  1.706912e-01  3.790624e-01 -2.141793e-01 -5.033792e-01  2.426439e-02
1936 -1.499829e-01 -4.709321e-02 -5.685531e-02  1.981667e-01  2.353384e-01
1937 -5.305823e-01 -1.738699e-01  1.291833e-01  1.501383e-03 -1.648938e-01
1938 -4.675644e-02 -2.106905e-01  7.750340e-02 -4.234799e-02 -2.210396e-01
1939  3.333940e-02 -2.064353e-01  1.683528e-01  3.776290e-01  1.331839e-01
1940 -3.272108e-01 -7.667727e-02  1.143320e-01  2.409685e-01 -5.393414e-02
1941  1.609808e-04  2.520528e-02  7.966475e-02  3.582103e-01 -3.745282e-01
1942 -2.105621e-01 -1.423219e-01 -1.407671e-01 -2.398250e-02 -2.552821e-01
1943 -4.405427e-02  2.563151e-03 -1.469047e-01  4.634041e-01 -4.738079e-01
1944 -2.183619e-02 -8.320794e-02 -2.921771e-02  1.956457e-01 -3.630967e-01
1945 -1.698236e-02 -8.739679e-02 -1.418986e-01 -4.004576e-01 -2.785992e-02
1946 -8.839638e-02 -1.133921e-01  7.855637e-02 -1.785497e-01  3.233297e-01
1947 -1.139764e-01 -1.611775e-02  1.462319e-01  3.479846e-01  8.894095e-02
1948  7.518810e-02 -2.326357e-01 -9.972051e-02 -3.176611e-01  4.243752e-01
1949 -1.184598e-01 -3.133870e-02  4.284637e-02  4.120314e-01  2.370064e-01
1950 -2.864985e-01 -1.599167e-02 -5.282667e-02 -3.755754e-01 -2.621055e-02
1951 -1.591443e-01 -5.538402e-02 -1.477331e-01  1.836240e-01  2.356696e-01
1952 -4.855685e-03 -5.467704e-02 -1.381822e-01  2.903710e-01  1.664290e-01
1953  5.194858e-02  6.656803e-02 -1.502567e-01 -3.414065e-01  1.565815e-01
1954 -1.588315e-01  1.653662e-01 -1.426590e-01 -6.693839e-01 -4.614976e-03
1955 -1.399330e-01 -5.993195e-02 -1.691378e-01 -1.600370e-01 -2.530214e-01
1956 -6.693086e-02 -1.099230e-01 -5.780330e-02  2.638718e-01  1.890978e-01
1957  3.256565e-01  1.014507e-01 -1.299792e-01 -1.702829e-01  5.556314e-01
1958  1.557201e-01  5.806317e-02  1.576609e-01  8.294779e-02  2.122073e-01
1959  6.401319e-02 -1.684218e-01  3.073768e-03 -3.505305e-02  2.343356e-02
1960 -6.637268e-02  1.129964e-02  1.271617e-02  2.927019e-01 -1.696833e-01
1961  1.668581e-01 -8.044133e-03  5.493180e-02  1.027905e-01  4.585702e-02
1962  2.110816e-01  4.557641e-01 -4.371250e-01  3.939627e-01 -2.135676e-01
1963  3.826947e-02  3.808115e-01  4.740467e-02 -1.697578e-01 -1.281356e-01
1964  7.592362e-02  2.562593e-02 -6.675663e-02 -1.396830e-01 -1.583550e-01
1965  8.885925e-02  1.072119e-01  6.978780e-02  3.970724e-02  4.108524e-02
1966 -8.178084e-02  3.492787e-02  5.506327e-02  3.611153e-01  2.329127e-02
1967  2.532721e-02  8.048379e-02 -5.098134e-02 -3.171424e-01  1.693669e-01
1968  4.253393e-01  1.508643e-01  3.633916e-01 -5.334193e-01  7.865000e-02
1969 -9.929665e-03  6.059335e-02 -3.533855e-02  2.927670e-01  6.606432e-03
1970 -9.545309e-02  1.005926e-01  1.112506e-02 -2.606569e-01 -2.417743e-01
1971  1.385822e-01  2.470989e-01 -1.361118e-01 -6.551537e-02  2.614472e-01
1972 -3.752375e-02  1.390318e-01  5.919686e-01 -2.046261e-01  2.526680e-01
1973  1.385134e-01 -6.146881e-02  3.833664e-02 -7.366117e-02  4.115909e-02
1974  6.048914e-02  3.454127e-02  4.513380e-02  2.632911e-01  1.417339e-01
1975 -5.750201e-02  2.258386e-02 -4.350287e-02 -3.064058e-01 -1.097118e-01
1976  2.562484e-02  2.797923e-02 -4.199140e-02  2.571136e-01  3.260860e-01
1977  1.097080e-01  1.413908e-01  1.503646e-02  1.246058e-01 -8.442757e-02
1978  8.338447e-03 -3.973398e-02  2.024498e-01  7.430409e-02 -2.237706e-01
1979 -7.385170e-02 -5.988406e-02  2.829998e-01 -3.480068e-01  7.822072e-02
1980 -1.925261e-01 -4.482000e-02  6.006344e-02  1.987021e-01  5.739316e-02
1981  3.494699e-01  1.758681e-02  4.795265e-03 -2.057843e-01  1.031290e-02
1982 -1.295020e-01  1.726459e-01 -4.691558e-02 -4.965449e-01  2.153010e-01
1983  5.702008e-02  9.658362e-02  2.951005e-01 -1.127614e-01 -1.920073e-01
1984  3.893655e-01 -4.876059e-03  2.014093e-01 -4.182497e-02 -5.502572e-01
1985 -4.719049e-02 -2.057526e-02  1.221452e-01  2.610693e-01  5.919898e-02
1986  1.419888e-01  4.394951e-02  4.802117e-01 -8.802753e-02 -2.833737e-01
1987  2.186597e-01  4.059202e-02  3.702811e-01 -1.288066e-02  5.142783e-03
1988 -1.700258e-01  3.127982e-02  1.905478e-01  4.055424e-01  5.641129e-02
1989 -1.750462e-02 -1.101529e-01 -1.414288e-02  2.332095e-01  2.996384e-03
1990  1.173560e-01 -2.201329e-01  1.249404e-01  5.211622e-01 -6.401760e-02
               Jun           Jul           Aug           Sep           Oct
1912 -1.202146e-01 -2.803713e-02  2.233733e-01 -1.752565e-01  2.622513e-02
1913  2.690574e-01 -6.057507e-02  4.087512e-01  1.126472e-01 -3.561219e-01
1914  2.898698e-02  1.902480e-01 -7.338789e-02 -1.376321e-01  1.335855e-01
1915 -2.540459e-01  2.082256e-01  1.186783e-01 -3.696631e-01  6.025071e-02
1916 -5.011390e-02  1.756759e-01 -1.037972e-02 -8.524152e-02 -1.291617e-01
1917  7.355925e-02  5.703068e-02 -7.108466e-02 -1.423159e-01  2.040347e-01
1918  1.373858e-01  1.557848e-01  2.826005e-02 -6.676824e-02 -1.771807e-01
1919  2.704738e-02  2.662001e-01  1.029624e-01 -1.805426e-01 -2.002980e-01
1920 -2.881611e-02  5.026379e-01  2.099146e-02 -4.542309e-02  3.330792e-01
1921  2.590800e-01 -1.487811e-02  4.594751e-02  2.076856e-03  2.582504e-01
1922  9.972273e-02 -1.542273e-01 -1.022915e-02  7.840095e-02  1.194174e-01
1923  1.399698e-01 -5.111860e-02 -3.117602e-02  6.575656e-02 -4.621102e-01
1924 -2.153841e-01 -1.769803e-02  1.653629e-01  2.007175e-01 -1.848261e-01
1925  2.382071e-02 -6.676082e-02 -5.231161e-02  1.166957e-01 -5.576425e-01
1926 -3.524365e-01  1.166507e-01 -1.571206e-01 -1.427060e-01  5.993417e-02
1927  7.093142e-02 -3.119283e-02 -2.467673e-02  4.437430e-02  3.600082e-01
1928 -1.838322e-02  6.251838e-02 -1.269100e-01 -2.158108e-01 -1.223446e-01
1929 -1.029336e-01 -2.774244e-01  4.181095e-02 -9.285818e-02 -9.624925e-02
1930  5.077680e-02  1.702640e-02 -9.922748e-02  1.050590e-02 -2.547496e-01
1931 -1.784442e-01  3.565084e-02 -1.357435e-01  5.496140e-02  2.604526e-02
1932  4.011842e-02 -5.530825e-02  1.557837e-01 -7.485458e-02 -1.661912e-02
1933  8.944173e-02  2.850927e-01  1.060835e-01 -9.671990e-02  2.432258e-03
1934 -2.748280e-02 -4.643543e-02  1.020571e-01  1.109698e-01  1.811410e-01
1935 -1.101294e-01  1.373210e-01 -1.008135e-01 -4.584641e-02 -1.796651e-01
1936  2.273690e-02 -8.447749e-02 -8.750893e-02  3.603283e-02  1.168324e-01
1937  2.453657e-02 -8.001239e-02 -4.317106e-02  1.153736e-01 -2.106405e-01
1938 -1.592959e-01 -1.452031e-01 -1.832604e-01  1.594965e-01 -3.193678e-01
1939 -3.935457e-02  9.193839e-02 -3.174929e-03 -4.654706e-02  1.747356e-01
1940 -1.031797e-01  1.757107e-02  4.945885e-02  4.060456e-02 -1.007948e-03
1941 -2.425885e-01 -5.117404e-02 -2.948433e-02  3.174737e-01  3.993207e-01
1942 -6.703813e-02 -7.693244e-02 -7.262046e-04 -1.394020e-01  5.373566e-02
1943  4.612135e-02  1.327843e-01 -4.248265e-02 -1.467874e-01 -9.447438e-02
1944 -1.039380e-01 -2.699738e-01  2.159153e-01  1.204964e-01  2.068312e-01
1945 -9.958986e-02 -2.470953e-01 -1.168399e-01 -6.988819e-02 -1.050313e-01
1946 -3.600342e-02 -3.705854e-02 -6.837567e-02 -1.999755e-01 -3.409423e-01
1947  8.900721e-02 -9.381864e-03 -8.268189e-02 -3.400417e-02  1.598462e-01
1948  2.684652e-01 -3.393429e-01  3.201265e-01  1.834571e-01  4.354448e-02
1949 -9.006497e-02 -1.431996e-01  1.996554e-01 -9.776569e-02 -6.817774e-03
1950  1.854538e-01 -1.399461e-02 -1.978122e-01 -6.389357e-02 -1.582617e-01
1951 -1.550082e-01  7.148529e-02 -1.774093e-01 -2.361388e-01 -7.276339e-02
1952  9.561457e-03  1.154318e-01 -1.215320e-01 -1.627866e-01 -1.799888e-02
1953 -2.403374e-01 -2.666028e-03 -1.149180e-01  1.473896e-01 -3.756548e-02
1954 -4.277458e-02  1.785317e-01  3.783343e-02  1.562748e-01 -4.101380e-02
1955  1.746120e-01  2.147978e-01 -4.171627e-02 -2.594388e-01 -3.549588e-02
1956  1.277255e-01 -1.467581e-01 -1.566598e-01 -2.229309e-02  1.035079e-01
1957 -2.009198e-01 -7.514927e-02  1.049863e-01  1.073800e-01 -2.156733e-01
1958  1.503477e-02 -2.302792e-01 -7.240577e-02  1.464299e-01  3.693583e-01
1959  6.104185e-02  9.937913e-02 -7.689098e-02  5.087359e-01 -5.210581e-02
1960  1.049451e-01  2.345201e-01 -1.358140e-01  1.928290e-01  7.017317e-02
1961  1.186213e-01 -2.797219e-01 -7.213172e-03  2.601062e-01  1.714685e-01
1962  1.443756e-01  8.554226e-02  1.658879e-01 -4.269605e-02  2.551728e-01
1963 -6.234988e-02 -2.947931e-02  5.925672e-02  1.846672e-01  1.370089e-02
1964  3.965558e-01  3.307166e-02  9.390725e-02  8.705444e-02  3.144259e-01
1965  5.239422e-02 -1.102085e-01  9.234569e-02 -7.598318e-02  3.113498e-01
1966  8.112159e-02  8.877706e-02  3.065916e-02 -2.806065e-05  1.897854e-01
1967  2.466878e-01 -7.069238e-02 -1.124010e-01 -8.848577e-03  3.402421e-02
1968 -3.277706e-02  1.968847e-01 -1.344176e-01  2.197119e-01 -1.093057e-01
1969 -4.965164e-03 -2.138298e-01  1.056325e-01  2.319791e-01  1.400778e-01
1970 -5.158920e-02 -3.692680e-01 -9.286558e-02  1.760737e-02 -1.912210e-02
1971  8.638631e-03 -9.380319e-04  2.157335e-03 -8.883692e-03  7.239712e-03
1972  3.118920e-01  7.743355e-03 -5.803339e-02 -1.509193e-01  7.233543e-02
1973 -1.414996e-01  7.950575e-03 -1.116547e-01 -2.004636e-01  4.028870e-01
1974  2.092732e-01  2.016992e-01 -1.562025e-02 -1.255940e-01  2.026512e-02
1975 -4.475951e-02  8.734588e-02 -1.026225e-01 -2.417311e-03  9.090727e-03
1976  9.214029e-03  3.753047e-01  3.545975e-01  1.847864e-01 -1.597822e-01
1977 -1.649375e-01  3.249929e-02  1.257900e-01 -2.783384e-02 -5.601774e-02
1978 -1.217191e-01 -6.758387e-02 -2.562966e-02  2.260764e-01 -5.410701e-02
1979 -1.841141e-01 -4.253111e-02 -2.059831e-01 -2.813471e-02 -1.464405e-01
1980 -3.137598e-01 -2.703491e-02 -2.035204e-02  2.920754e-01 -7.364804e-02
1981 -1.648135e-01 -2.280137e-02  1.165201e-01 -1.218628e-01 -2.703769e-02
1982  6.637926e-02  1.295684e-01  1.154062e-01  1.889398e-01 -1.727285e-01
1983 -1.233023e-01  3.869405e-02  1.940881e-02 -5.106174e-02 -1.657570e-01
1984  3.744296e-02  1.675092e-01 -6.311491e-02  1.611361e-01  4.348891e-02
1985  1.044547e-01 -1.890907e-01 -1.133199e-01 -1.442031e-02  1.749806e-01
1986  2.297531e-01 -1.990856e-01 -7.227606e-02 -1.535200e-01 -4.306682e-02
1987 -1.928576e-01 -1.471645e-01  5.978790e-02 -2.131642e-01 -2.232250e-01
1988 -8.362957e-02 -6.479436e-02  6.164953e-03 -1.028996e-01  2.821337e-02
1989 -8.534829e-02 -1.992696e-01  1.365019e-01 -1.685848e-01  2.297495e-02
1990  3.549551e-01 -2.924441e-02 -1.506332e-01 -2.353447e-01  2.259642e-02
               Nov           Dec
1912 -2.023753e-01 -8.371192e-02
1913 -3.563444e-01 -8.110854e-02
1914  1.139835e-01 -1.114747e-01
1915  5.381637e-02 -4.329405e-01
1916 -2.645437e-01 -2.380060e-01
1917  1.631487e-01  2.027358e-01
1918 -1.520926e-01 -6.843971e-02
1919  6.797975e-02  1.743626e-01
1920 -2.222222e-01 -4.729552e-02
1921 -2.644246e-02  4.648648e-02
1922 -2.981411e-01  1.886132e-01
1923 -1.948645e-01  1.065701e-01
1924 -1.736052e-01  2.386236e-01
1925 -1.507200e-01  8.469582e-01
1926  1.888699e-02 -7.084517e-02
1927 -2.001024e-01 -1.460653e-01
1928 -2.885730e-01 -2.709626e-01
1929 -1.747114e-01  1.140587e-02
1930 -6.123198e-02 -5.212326e-02
1931 -1.215488e-01 -1.452958e-01
1932  2.465383e-01  1.636122e-01
1933  5.480525e-01 -3.243086e-03
1934  2.689330e-01 -1.194561e-01
1935 -5.697012e-02  9.610555e-02
1936  1.604938e-01  6.201187e-02
1937  2.431485e-01 -1.784854e-01
1938 -2.771129e-01  7.396836e-03
1939  2.183005e-01  5.816706e-01
1940 -2.050157e-01 -8.081577e-03
1941 -6.325106e-02  1.599149e-01
1942 -1.667850e-01  1.096391e-01
1943 -2.364824e-01 -1.094085e-01
1944 -3.279357e-02 -1.049793e-01
1945 -1.408098e-01 -5.111273e-02
1946 -2.809509e-01  7.737759e-02
1947 -5.690200e-02 -4.013909e-02
1948 -1.518133e-01 -3.095895e-01
1949  3.526678e-01 -2.698931e-02
1950  1.533514e-01  1.762746e-01
1951 -6.839538e-04 -7.012491e-02
1952 -3.478542e-01 -1.774476e-01
1953  2.418168e-01 -6.858480e-02
1954  3.427314e-01  9.720156e-02
1955 -6.328121e-02 -7.980323e-02
1956 -6.844017e-02  6.350043e-03
1957  2.409651e-01  2.428767e-01
1958 -2.457013e-01  1.854303e-01
1959  1.750241e-01  7.820218e-02
1960  2.120967e-02 -8.181141e-02
1961 -1.468061e-01 -2.700201e-01
1962  3.628659e-01  6.089297e-02
1963 -8.611982e-02  1.311099e-01
1964 -9.233234e-02 -8.129846e-02
1965  1.029483e-01 -9.087624e-02
1966 -7.199190e-02  2.649409e-01
1967  2.180664e-01 -6.796753e-02
1968  2.145288e-01 -8.866777e-02
1969  6.706357e-02  1.046292e-01
1970 -2.408416e-01  6.118401e-03
1971  1.819947e-02 -1.902634e-01
1972 -3.428856e-02 -6.931781e-02
1973 -9.893930e-03 -4.450927e-03
1974 -1.812127e-01  2.082858e-02
1975  4.150293e-01 -1.499411e-02
1976 -4.629606e-02  1.868597e-01
1977 -8.649529e-02  9.016773e-02
1978 -3.220429e-02 -1.027890e-01
1979 -2.899158e-01  2.473983e-01
1980 -3.740064e-03  5.105995e-01
1981  4.071851e-01 -1.338013e-01
1982 -1.861787e-01  5.009710e-02
1983  4.873755e-01 -4.322056e-01
1984 -3.341521e-01 -1.514237e-01
1985 -2.481359e-01 -2.144634e-01
1986  6.220532e-02 -8.177442e-02
1987  2.358583e-01 -1.187045e-01
1988  1.197035e-01 -1.311440e-01
1989  5.399037e-01  3.786655e-02
1990  4.909906e-01 -1.496410e-01

$portmanteau.test
$portmanteau.test$QM
           [,1]      [,2]      [,3]     [,4]
 [1,] 1.2385593  7.662516  8.557323 12.67232
 [2,] 6.7037426 10.314739 19.925393 29.65042
 [3,] 4.4260039  6.286687 12.741855 22.10372
 [4,] 7.0814729  7.953657 12.343296 16.23929
 [5,] 1.2756624  3.519195 15.541614 20.53343
 [6,] 0.3345657 14.774391 18.576333 23.05116
 [7,] 2.7661078 10.266698 14.730405 17.24386
 [8,] 4.5565922 11.572028 14.379916 17.55193
 [9,] 4.7421034  7.700167 13.178117 14.25953
[10,] 1.8503846  6.016364 13.748339 19.26425
[11,] 2.7374340  6.952487  8.354099 16.61374
[12,] 7.5349809 15.032765 26.068905 35.15483

$portmanteau.test$QM.df
      [,1] [,2] [,3] [,4]
 [1,]    4    9   14   19
 [2,]    4    9   14   19
 [3,]    4    9   14   19
 [4,]    4    9   14   19
 [5,]    4    9   14   19
 [6,]    2    7   12   17
 [7,]    3    8   13   18
 [8,]    4    9   14   19
 [9,]    4    9   14   19
[10,]    2    7   12   17
[11,]    4    9   14   19
[12,]    4    9   14   19

$portmanteau.test$QM.sl
           [,1]       [,2]       [,3]       [,4]
 [1,] 0.8717102 0.56848115 0.85832122 0.85491505
 [2,] 0.1523971 0.32561132 0.13251121 0.05641935
 [3,] 0.3514119 0.71091781 0.54694342 0.27912456
 [4,] 0.1316449 0.53882312 0.57875437 0.64125736
 [5,] 0.8654910 0.94012295 0.34216070 0.36314375
 [6,] 0.8459603 0.03900261 0.09927870 0.14759244
 [7,] 0.4291096 0.24680395 0.32448403 0.50640302
 [8,] 0.3358898 0.23852513 0.42180755 0.55252930
 [9,] 0.3147971 0.56462153 0.51254894 0.76835716
[10,] 0.3964552 0.53783990 0.31706680 0.31357700
[11,] 0.6026802 0.64206631 0.87007477 0.61601782
[12,] 0.1101766 0.09003991 0.02536967 0.01337899


$residual.acf
           lags
periods             lag 1         lag 2        lag 3        lag 4        lag 5
  period 1  -9.074425e-02  1.273701e-02  0.041466695  0.073403977  0.013077003
  period 2   5.430577e-02 -2.458664e-01  0.127661923  0.070487889  0.014692426
  period 3  -1.163953e-01  1.594117e-01 -0.043457572  0.060937812 -0.106053752
  period 4   1.258787e-01 -2.221958e-01  0.023543959  0.149194025 -0.036154937
  period 5  -3.926900e-02  2.157657e-02  0.010352620  0.070126997  0.094866588
  period 6   7.061298e-17 -1.621368e-16 -0.051544675 -0.039689166  0.001710566
  period 7   5.096794e-03 -1.134987e-02  0.009973078 -0.169991576  0.076567798
  period 8  -2.522742e-02  6.219444e-02  0.038789593  0.060271993 -0.219172227
  period 9   1.128500e-01 -1.514618e-01 -0.031995535  0.004317709 -0.152671045
  period 10 -2.019760e-16  3.606214e-16 -0.032783424  0.118472296 -0.091171005
  period 11  8.528105e-02 -1.052427e-01  0.092714190  0.076690084 -0.042718697
  period 12 -2.769031e-02 -1.679117e-01  0.257622467 -0.004649663  0.005239010
           lags
periods           lag 6       lag 7        lag 8       lag 9       lag 10
  period 1  -0.07997898  0.20316707 -0.169840857 -0.06646055  0.019134506
  period 2   0.16695454  0.06222316 -0.013248934  0.08808317  0.077598889
  period 3   0.05277002 -0.05003146 -0.081047044  0.08558261  0.063827793
  period 4  -0.09922215  0.01735967 -0.001327322 -0.02710302 -0.004222671
  period 5  -0.02491033 -0.03054336  0.001776585 -0.14466338 -0.074535888
  period 6  -0.16244332  0.09084480  0.355089220 -0.05793567  0.127997625
  period 7   0.11959298  0.10288826  0.207407104 -0.11327220 -0.114833043
  period 8   0.25759068 -0.06312977 -0.083522088  0.01676992  0.104755702
  period 9  -0.04550089  0.16848808 -0.023851623  0.07264836  0.032517331
  period 10  0.14312125  0.04976958 -0.017740522  0.16666508 -0.040742566
  period 11  0.12251533  0.11091475  0.105492581  0.02978174  0.118437230
  period 12 -0.10946470  0.24630913  0.051528421 -0.13967105  0.009734803
           lags
periods          lag 11       lag 12       lag 13       lag 14       lag 15
  period 1   0.09808334 -0.028347279 -0.008849588 -0.026495795 -0.009408534
  period 2  -0.07525990  0.192862120  0.250270912 -0.007721045  0.122179835
  period 3  -0.05501715  0.239858813  0.082921108  0.106376562 -0.021520244
  period 4  -0.01933725 -0.160597593  0.093705556 -0.134642835 -0.033671927
  period 5   0.15656141  0.199839163 -0.239089776 -0.158536443  0.050002317
  period 6   0.02501159 -0.002585942 -0.040052012 -0.157217219 -0.143397355
  period 7   0.04015840  0.183130160 -0.037297456  0.012261713 -0.135083520
  period 8  -0.03157999  0.127517652  0.103748448  0.009790310  0.081016478
  period 9   0.00355698  0.226035553 -0.084950125  0.052275606 -0.078204518
  period 10 -0.01543402  0.057475849  0.008101748 -0.041028067  0.302092614
  period 11  0.03868042  0.059960660 -0.050321882  0.092970491  0.034045071
  period 12 -0.21956514  0.161023994 -0.103066245 -0.134065241  0.187482676
           lags
periods           lag 16       lag 17      lag 18       lag 19       lag 20
  period 1  -0.108914086  0.008288044  0.17558821  0.056728707  0.073643519
  period 2   0.217806193  0.115035044 -0.09743203  0.007045642  0.226423696
  period 3  -0.107091220 -0.065376609  0.13094330  0.078637840 -0.276463119
  period 4  -0.007679860  0.153199803 -0.10252187  0.118237053  0.006926512
  period 5  -0.005615818 -0.072931798  0.03825222 -0.096617663 -0.213165434
  period 6   0.186012735  0.052686998 -0.08031297  0.049760738  0.096879508
  period 7  -0.152161409 -0.012084065 -0.01359687  0.061578180 -0.063526946
  period 8   0.019116873  0.039695453 -0.04352545  0.171589208  0.079269504
  period 9   0.066163208  0.022958996 -0.01608694  0.085179857  0.033112301
  period 10  0.094002988 -0.090349447  0.14782214  0.129534191  0.115359281
  period 11 -0.110827346  0.170414619  0.22727146  0.004984024  0.101133507
  period 12 -0.001607617 -0.134820673 -0.18064329  0.183606985 -0.170391233

$residual.acf.sd
           lags
periods          lag 1       lag 2      lag 3      lag 4     lag 5     lag 6
  period 1  0.08633936 0.093938065 0.10598928 0.10650102 0.1131185 0.1119606
  period 2  0.08611677 0.098572324 0.10251300 0.10909916 0.1093871 0.1131645
  period 3  0.08819503 0.096846801 0.10380263 0.10609313 0.1100061 0.1101794
  period 4  0.08559165 0.099166597 0.10373310 0.10755605 0.1088418 0.1110672
  period 5  0.06496980 0.104307688 0.10824256 0.10966048 0.1108818 0.1112994
  period 6  0.00766863 0.004428359 0.08549513 0.09912249 0.1037048 0.1075404
  period 7  0.04965632 0.034367519 0.09742581 0.11168745 0.1120745 0.1122172
  period 8  0.07163479 0.092393197 0.11245332 0.10802872 0.1125081 0.1125084
  period 9  0.08736839 0.090107961 0.10085991 0.11247534 0.1098291 0.1125084
  period 10 0.01652553 0.012832852 0.07118343 0.09220197 0.1124528 0.1079895
  period 11 0.08276627 0.085136741 0.11210596 0.10776766 0.1099378 0.1125011
  period 12 0.07663214 0.099818618 0.10073928 0.11232208 0.1103346 0.1113234
           lags
periods         lag 7     lag 8     lag 9    lag 10    lag 11    lag 12
  period 1  0.1125356 0.1132256 0.1130622 0.1132277 0.1132277 0.1132277
  period 2  0.1124965 0.1128279 0.1132265 0.1131320 0.1132277 0.1132277
  period 3  0.1124702 0.1120629 0.1122648 0.1125081 0.1124504 0.1125088
  period 4  0.1111666 0.1124865 0.1122509 0.1123677 0.1125084 0.1124750
  period 5  0.1120301 0.1120630 0.1125013 0.1124229 0.1124617 0.1125086
  period 6  0.1088303 0.1110627 0.1111624 0.1124864 0.1122501 0.1123672
  period 7  0.1123414 0.1123842 0.1124593 0.1124627 0.1125080 0.1124999
  period 8  0.1125086 0.1125087 0.1125087 0.1125087 0.1125088 0.1125088
  period 9  0.1125086 0.1125086 0.1125087 0.1125087 0.1125088 0.1125088
  period 10 0.1125081 0.1125084 0.1125085 0.1125087 0.1125087 0.1125087
  period 11 0.1118979 0.1125087 0.1125087 0.1125088 0.1125088 0.1125088
  period 12 0.1125052 0.1122258 0.1125087 0.1125088 0.1125088 0.1125088
           lags
periods        lag 13    lag 14    lag 15    lag 16    lag 17    lag 18
  period 1  0.1132277 0.1132277 0.1132277 0.1132277 0.1132277 0.1132277
  period 2  0.1132277 0.1132277 0.1132277 0.1132277 0.1132277 0.1132277
  period 3  0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 4  0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 5  0.1124975 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 6  0.1125084 0.1124749 0.1125088 0.1125088 0.1125088 0.1125088
  period 7  0.1125039 0.1125088 0.1125076 0.1125088 0.1125088 0.1125088
  period 8  0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 9  0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 10 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 11 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
  period 12 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088 0.1125088
           lags
periods        lag 19    lag 20
  period 1  0.1132277 0.1132277
  period 2  0.1132277 0.1132277
  period 3  0.1125088 0.1125088
  period 4  0.1125088 0.1125088
  period 5  0.1125088 0.1125088
  period 6  0.1125088 0.1125088
  period 7  0.1125088 0.1125088
  period 8  0.1125088 0.1125088
  period 9  0.1125088 0.1125088
  period 10 0.1125088 0.1125088
  period 11 0.1125088 0.1125088
  period 12 0.1125088 0.1125088

$cov
$cov$`period 1`
            [,1]
[1,] 0.004110686

$cov$`period 2`
            [,1]
[1,] 0.004666186

$cov$`period 3`
            [,1]
[1,] 0.006086609

$cov$`period 4`
           [,1]
[1,] 0.01481656

$cov$`period 5`
            [,1]
[1,] 0.004509269

$cov$`period 6`
              [,1]         [,2]          [,3]
[1,]  0.0063280375 -0.001095628 -0.0004168932
[2,] -0.0010956277  0.003556099 -0.0025039456
[3,] -0.0004168932 -0.002503946  0.0059392389

$cov$`period 7`
             [,1]         [,2]
[1,]  0.011010825 -0.002037675
[2,] -0.002037675  0.006483237

$cov$`period 8`
            [,1]
[1,] 0.004697961

$cov$`period 9`
            [,1]
[1,] 0.007931057

$cov$`period 10`
             [,1]        [,2]         [,3]
[1,]  0.018649200 -0.01664179  0.003292144
[2,] -0.016641792  0.04366329 -0.024571970
[3,]  0.003292144 -0.02457197  0.027518820

$cov$`period 11`
            [,1]
[1,] 0.008324338

$cov$`period 12`
            [,1]
[1,] 0.005059931

pear documentation built on May 29, 2017, 11:40 p.m.