MFDFA procedure explained!

README.md

@@ -8,24 +8,25 @@ In what follows, I outline the MFDFA procedure, according to _Kantelhardt, 2002_
 
 Given a series $X = x(1), x(2), \cdots, x(N)$, MFDFA processes the series as follows: 
 1-	  Build the profile of the series by subtracting the mean and computing the cumulative sum:
-    \begin{equation}
+    $$
         Y(i) = \sum_{k=1}^{i} [x(k) - \langle X\rangle], i=1, \cdots, N
-    \end{equation}
+    $$
     in which $\langle X\rangle$ is the mean of $X$.
 
 2-	  Divide the profile of the series into $N_s=N/s$ windows for different values of $s$, which is the size of windows.
     As the length of the series, $N$, may not be always divisible by $s$ and a portion of the series in the end may be excluded from the computation, the windowing procedure is repeated starting from the end. As a result, the number of windows increases to $2 \times N_s$.
 
 3-	 Detrend the values in each window $v$, $v=1,\cdots,2\times N_s$, by subtracting the best fitting line, $Y'$, and calculate the mean square fluctuation of residuals:
-    \begin{equation}
+    $$
         F^2(s, v)=\frac{1}{s}\sum_{i=1}^{s}[Y(s \times (v-1) + i)-Y'(s \times (v-1) + i)]^2
-    \end{equation}
+    $$
 
 4-	 Calculate the $q$th order of the mean square fluctuations:
-    \begin{equation}
+    $$
         F_q(s) = \{\frac{1}{2\times N_s}\sum_{v=1}^{N_s}[F^2(s, v)]^{q/2}\}^{1/q}
-    \end{equation}
-5-	 Compute the growth factor of fluctuations, $h(q)$, using a log-log regression on $F_q(s)$ values, i.e. $ \log F_q(s)\sim h(q) \times \log s$
+    $$
+
+5-	 Compute the growth factor of fluctuations, $h(q)$, using a log-log regression on $F_q(s)$ values, i.e. $\log F_q(s)\sim h(q) \times \log s$
 \end{enumerate}