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52 | 52 | disp('This type of wavelet transform does not apply!')
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53 | 53 | end
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54 | 54 |
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55 |
| -% disp(['Additive:' num2str(sum(abs(sum(X_WT,2)-X_tmp)))]) |
56 |
| -% disp(['Variance:' num2str(sum(var(X_WT))-var(X_tmp))]) |
57 |
| - |
58 | 55 | %standardization w.r.t. observed period
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59 | 56 | X_WT_n = X_WT(1:N,:);
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60 |
| - %X_WT_norm=(X_WT-mean(X_WT_n))./std(X_WT_n); |
61 | 57 |
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62 | 58 | % alternative way to standardize data for older matlab versions
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63 |
| - %subtract mean of each column |
| 59 | + % subtract mean of each column |
64 | 60 | X_WT_c=X_WT-repmat(mean(X_WT_n),num_obs,1);
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65 |
| - %divide by the standard deviation of each column |
| 61 | + % divide by the standard deviation of each column |
66 | 62 | X_WT_norm=X_WT_c./repmat(std(X_WT_n,0,1),num_obs,1);
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67 |
| -% disp(sum(abs(X_WT_norm1-X_WT_norm))) |
68 |
| - |
69 |
| -% disp(var(X_WT_norm(1:N,:))) |
70 |
| -% disp(mean(X_WT_norm(1:N,:))) |
71 |
| -% disp(sum(abs(normalize(X_WT_n)-X_WT_norm(1:N,:)))) |
72 |
| - |
73 |
| - %corr1 = corrcoef([Y X_WT(1:length(Y),:)]) ; %correct |
74 |
| - %corr1 = cov([Y X_WT(1:length(Y),:)]) ; %wrong |
75 |
| - %C(:,i_var) = corr1(1,2:lev+2); |
76 | 63 |
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| 64 | + |
77 | 65 | % covariance - Eq. 10 in WRR2020 paper
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78 |
| - %corr = 1/(N-1)*Y'*X_WT_norm(1:N,:); |
79 |
| - |
80 |
| - %corr = 1/(length(Y)-1)*Y'*normalize(X_WT(1:length(Y),:)); |
81 |
| - %disp(normalize(corr1(1,2:lev+2),'norm') - normalize(corr,'norm')) |
82 | 66 | C(:,i_var) = 1/(N-1)*Y'*X_WT_norm(1:N,:);
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83 | 67 |
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84 | 68 | % normalization to get unit norm
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85 |
| - %C_norm = normalize(C(:,i_var),'norm') ; |
86 | 69 | C_norm = C(:,i_var)./sqrt(sum(C(:,i_var).^2)) ;
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87 |
| -% disp(norm(C_norm)) |
88 |
| -% disp(norm(C(:,i_var))-sqrt(sum(C(:,i_var).^2))) |
89 | 70 |
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90 | 71 | % variance transformation - Eq. 9 in WRR2020 paper
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91 |
| - %X_WaSP(:,i_var) = normalize(X_WT)*(std(X(:,i_var)).*C_norm(:)) ; |
92 | 72 | X_WaSP(:,i_var) = X_WT_norm*(std(X(1:N,i_var)).*C_norm) ;
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93 | 73 |
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94 |
| - X_WT_norm'*X_WT_norm |
95 | 74 | % maintain the original trend of the variable
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96 | 75 | if flag_sign
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97 | 76 | [rho, pval] = corr(X_WaSP(:,i_var),X_tmp);
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