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whittle's log-likelihood function with arfima (0,d,0) theoretical psd function  (MathWorks Inc)


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    MathWorks Inc whittle's log-likelihood function with arfima (0,d,0) theoretical psd function
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Whittle's Log Likelihood Function With Arfima (0,D,0) Theoretical Psd Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pmc10662130-120-38-33
    Average 90 stars, based on 1 article reviews
    whittle's log-likelihood function with arfima (0,d,0) theoretical psd function - by Bioz Stars, 2026-09
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    1) Product Images from "A guide to Whittle maximum likelihood estimator in MATLAB"

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    Journal: Frontiers in Network Physiology

    doi: 10.3389/fnetp.2023.1204757

    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Figure Legend Snippet: Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.

    Techniques Used: Generated

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .
    Figure Legend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .

    Techniques Used:

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.
    Figure Legend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.

    Techniques Used:

    Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.
    Figure Legend Snippet: Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.

    Techniques Used:

    Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.
    Figure Legend Snippet: Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.

    Techniques Used:

    Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.
    Figure Legend Snippet: Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.

    Techniques Used:

    Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( <xref ref-type= Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5." title="Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait ..." property="contentUrl" width="100%" height="100%"/>
    Figure Legend Snippet: Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5.

    Techniques Used: Comparison

    log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .
    Figure Legend Snippet: log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .

    Techniques Used: Generated

    Related Articles

    Generated:

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB
    Article Snippet: at the end of the mother code whittle.m (as is the case with the provided code) or in two separate files that can be named WLLFfgn.m and WLLFarf.m . .. .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf . .. The outputs are lwHfgn for code 6 and lwHarf for code 7 and correspond to l W H in Equation .

    Comparison:

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB
    Article Snippet: at the end of the mother code whittle.m (as is the case with the provided code) or in two separate files that can be named WLLFfgn.m and WLLFarf.m . .. .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf . .. The outputs are lwHfgn for code 6 and lwHarf for code 7 and correspond to l W H in Equation .



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    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Generated

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( <xref ref-type= Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5." width="100%" height="100%">

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Comparison

    log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Generated