使用Swift进行峰值检测以获取生长时间序列 [英] peak detection for growing time series using Swift

问题描述

有人会使用Swift（v3）拥有一个很好的算法来测量增长的时间序列数据中的峰值吗？因此，请在数据流入时检测峰值。

例如

样本数据集（最后一个系列的摘要）：

 让样本= [ 0.01，-0.02，-0.02、0.01，-0.01，-0.01、0.00、0.10、0.31，
 -0.10，-0.73，-0.68、0.21、1.22、0.67，-0.59，-1.04、0.06、0.42 ，0.07，
 0.03，-0.18、0.11，-0.06，-0.02、0.16、0.21、0.03，-0.68，-0.89、0.18，
 1.31、0.66、0.07，-1.62，-0.16， 0.67，0.19，-0.42，0.23，-0.05，-0.01，
 0.03，0.06，0.27，0.15，-0.50，-1.18，0.11，1.30，0.93，0.16，-1.32，
 -0.10 ，0.55、0.23，-0.03，-0.23、0.16，-0.04、0.01、0.12、0.35，-0.38，
 -1.11、0.07、1.46、0.61，-0.68，-1.16、0.29、0.54，-0.05 ，0.02，-0.01，
 0.12、0.23、0.29，-0.75，-0.95、0.11、1.51、0.70，-0.30，-1.48、0.13，
 0.50、0.18，-0.06，-0。 01，-0.02，0.03，-0.02，0.06，0.03，0.03，0.02，
 -0.01，0.01，0.02，0.01] 
  

更新：感谢Jean-Paul提供的

完整数据集（应产生25个峰值）：

 让样本= [-1.38，-0.97，-1.20，-2.06，-2.26，-0.99，0.11，-0.47 ，-0.95，-2.61，-0.88，-0.74，-1.12，-1.19，-1.12，-1.04，-0.72，-1.21，-2.61，-1.41，-0.23，-0.27，-0.43，-1.77，- 2.75，-0.61，-0.73，-1.53​​，-1.02，-1.14，-1.12，-1.06，-0.78，-0.72，-2.41，-1.55，-0.01，-0.44，-0.47，-2.02，-1.66， -0.43，-0.93，-1.51，-0.86，-1.06，-1.10，-0.88，-0.84，-1.26，-2.59，-0.92，0.29，-0.50，-1.31，-2.40，-0 .88，-0.56，-1.09，-1.14，-1.09，-0.90，-0.99，-0.84，-0.75，-2.59，-1.34，-0.08，-0.36，-0.50，-1.89，-1.60，-0.55 ，-0.78，-1.46，-0.96，-0.97，-1.18，-0.98，-1.10，-1.07，-1.06，-1.79，-1.78，-1.54，-1.25，-1.00，-0.46，-0.27，- 0.20，-0.15，-0.13，-0.11，-0.13，-0.09，-0.09，-0.05、0.02、0.20，-0.31，-1.35，-0.03、1.34、0.52、0.80，-0.91，-1.26，-0.10 ，-0.10，0.53，0.93，0.60，-0.83，-1.87，-0.21，1.26，0.44，0.86，0.73，-2.05，-1.66，0.31，1.04，0.72，0.63，-0.01，-2.14，-0.48， 0.77、0.63、0.58、0.66，-1.01，-1.28、0.18、0.44、0.09，-0.27，-0.06、0.06，-0.18，-0.01，-0.08，-0.07，-0.06，-0.06，-0.07，- 0.07，-0.06，-0.05，-0.04，-0.03，-0.02，-0.02，-0.03，-0.03，-0.01、0.01、0.00、0.01、0.05、0.12、0.16、0.25、0.29，-0.16，-0.69 ，-1.05，-0.84，-0.54，-0.07，0.46，1.12，1.05，0.77，0.68，0.63，0.39，-0.96，-1.61，-0.68，-0.14，-0.03，0.22，0.31，0.15，-0.02 ，0.11、0.14、0.00、0.04、0.18、0.27、0.14，-0.05，-0.03，-0.08，-0.41，-0.94，-1.03，-0.50、0.02、0.52、1.10、1.03、0.79、0.69， 0.55，-0.34，-1.17，-0.89，-0.54，-0.22、0.37、0.47、0.39、0.23、0.00，-0.02、0.05、0.10、0.12、0.09、0.05，-0.12，-0.50，-0.89，- 0.89，-0.48、0.00、0.43、1.03、0.95、0.67、0.64、0.47，-0.07，-0.85，-1.02，-0.73，-0.08、0.38、0.46、0.32、0.15、0.01，-0.01、0.09、0.20 ，0.23、0.19、0.12，-0.50，-1.17，-0.97，-0.12、0.15、0.70、1.31、0.97、0.45、0.27，-0.73，-1.00，-0.52，-0.27、0.10、0.33、0.34、0.23 ，0.07，-0.04，-0.27，-0.24、0.10、0.21、0.05，-0.07、0.04、0.21、0.29、0.16，-0.45，-1.13，-0.93，-0.28、0.04、0.72、1.35、1.05、0.56 ，0.43、0.17，-0.59，-1.38，-0.76、0.10、0.44、0.46、0.35、0.12，-0.07，-0.05，-0.01，-0.07，-0.04、0.01、0.01、0.06、0.02，-0.03， -0.05、0.00、0.01，-0.02，-0.03，-0.02，-0.01、0.00，-0.01、0.00，-0.01、0.00，-0.01，-0.01、0.00、0.01，-0.01，-0.01、0.00、0.00 ，0.01、0.01、0.01、0.04、0.06、0.05、0.05、0.04、0.03、0.00，-0.12，-0.16，-0.09，-0.01、0.14、0.07、0.06、0.00，-0.03、0.00、0.06、0.06， -0.04，-0.11，-0.02、0.13、0.18、0.21、0.01，-0.31，-0.92，-1.35， -0.62，0.03，0.78，1.36，1.07，0.59，0.75，0.42，-1.65，-3.16，-0.97，0.24，1.44，1.50，0.84，0.47，0.56，0.40，-1.50，-2.71，-1.22，0.01 ，1.20，1.55，0.92，0.44，0.66，0.73，-0.43，-2.34，-2.28，-0.72，0.36，1.41，1.56，0.89，0.54，0.67，0.39，-1.78，-2.75，-1.07，-0.07 ，1.16、1.65、0.80、0.47、0.73、0.86，-0.24，-1.52，-1.68，-0.39、0.02、0.38、0.60、0.49、0.02，-0.42，-0.31，-0.01、0.08、0.00，-0.07 ，-0.05，-0.01，-0.02，-0.04，-0.05，-0.02，-0.01，-0.02，-0.02，-0.03，-0.05，-0.04，-0.03，-0.01，-0.01、0.00，-0.01 ，0.00、0.01、0.00、0.00、0.00、0.01、0.01，-0.01，-0.03，-0.02，-0.01、0.00、0.00、0.00，-0.01、0.01、0.00，-0.01、0.02、0.07、0.15、0.28 ，0.31、0.08，-0.26，-0.54，-0.96，-1.08，-0.27、0.01、0.45、1.18、1.07、0.71、0.65、0.20，-0.80，-1.30，-0.74，-0.24、0.29、0.47， 0.34、0.15、0.02、0.03，-0.02，-0.16，-0.13、0.05、0.09，-0.01，-0.08，-0.06、0.03、0.13、0.19、0.23、0.18、0.10，-0.07，-0.44，-0.91 ，-1.05，-0.64，-0.08，0.50，1.12，1.35，0.89，0.58，0.54，-0.58，-1.27，-1 .20，-0.48、0.19、0.62、0.62、0.37，-0.01，-0.35，-0.33、0.07、0.29、0.10，-0.14，-0.10、0.07、0.07、0.01、0.03、0.09、0.20、0.32、0.26 ，-0.02，-0.32，-0.78，-1.25，-0.93，-0.16，0.30，0.88，1.40，1.14，0.72，0.48，-0.54，-1.21，-1.13，-0.41，0.18，0.51，0.53，0.36 ，0.11，-0.03，-0.09，-0.28，-0.11、0.11、0.15、0.04，-0.08，-0.04、0.04、0.09、0.16、0.26、0.43、0.09，-0.88，-1.46，-0.64，-0.16 ，0.43、1.37、1.34、0.84、0.52，-0.17，-0.87，-1.22，-0.76、0.03、0.47、0.60、0.36、0.04，-0.09，-0.03、0.02，-0.04、0.04、0.12、0.13， 0.19，0.27，0.31，0.18，-0.42，-0.99，-1.13，-0.75，-0.22，0.50，1.42，1.41，0.98，0.51，0.29，-0.69，-1.59，-0.88，-0.13，0.31，0.49 ，0.46、0.30、0.05，-0.08，-0.03、0.01，-0.04，-0.06、0.02、0.03、0.01，-0.02、0.01、0.04、0.06、0.04、0.03、0.02、0.03、0.03、0.01，-0.01 ，0.00，0.02，0.00，0.02，0.02，0.02，-0.02，-0.01，0.02，0.02，0.01，0.02，0.02，0.02，0.02，0.04，0.03，0.01，0.01，0.02，0.01，0.01，0.01，0.02 ，0.01、0.00、0.01、0.01、0.00、0.00、0.01、0.00、0.0 0、0.01、0.00、0.02、0.00、0.00、0.01、0.01、0.00、0.00、0.01、0.01、0.00、0.00、0.00、0.01、0.01、0.00、0.01、0.00、0.01、0.01、0.01、0.01、0.01， 0.01、0.00、0.00、0.00、0.00、0.00、0.00、0.00、0.01、0.01、0.01、0.00、0.00、0.00、0.00、0.00、0.00、0.00] 
  

因此，我不确定z-wave算法是否适合这种数据集。

解决方案

将平滑的z分数算法翻译为Swift

好吧，快速帮助您：这是将算法翻译成Swift：

更新

您可以通过对 lag 的滞后值使用不同的值来提高算法的性能平均值和标准偏差。例如：

  //平滑z分数阈值过滤器
 func ThresholdingAlgo（y：[Double]，lagMean：Int ，lagStd：Int，阈值：Double，影响均值：Double，influenceStd：Double）-> （[Int]，[Double]，[Double]）{
 
 //创建数组
 var signal = Array（重复：0，计数：y.count）
 var filterYmean = Array（重复：0.0，计数：y.count）
 varfilteredYstd = Array（重复：0.0，计数：y.count）
 var avgFilter = Array（重复：0.0，计数：y。 count）
 var stdFilter = Array（重复：0.0，count：y.count）
 
 //为0中的i初始化变量
 ... lagMean-1 {
信号[i] = 0 
filteredYmean [i] = y [i] 
filteredYstd [i] = y [i] 
} 
 
 //开始filter 
 avgFilter [lagMean-1] =算术平均值（array：subArray（array：y，s：0，e：lagMean-1））
 stdFilter [lagStd-1] = standardDeviation（array：subArray（ array：y，s：0，e：lagStd-1））
 
 for i in max（lagMean，lagStd）... y.count-1 {
如果abs（y [ i]-avgFilter [i-1]）> threshold * stdFilter [i-1] {如果y [i]大于
， avgFilter [i-1] {
 signals [i] = 1 //正信号
} else {
 signals [i] = -1 //负信号
} 
filteredYmean [i] = ImpactMean * y [i] +（1-influenceMean）* filteredYmean [i-1] 
filteredYstd [i] = ImpactStd * y [i] +（1-influenceStd）* filteredYstd [ i-1] 
} else {
 signal [i] = 0 //无信号
filteredYmean [i] = y [i] 
filteredYstd [i] = y [i ] 
} 
 //调整过滤器
 avgFilter [i] =算术平均值（array：subArray（array：filteredYmean，s：i-lagMean，e：i））
 stdFilter [i] = standardDeviation（array：subArray（array：filteredYstd，s：i-lagStd，e：i））
} 
 
 return（signals，avgFilter，stdFilter）
 } 
  

然后使用例如 let（signals，avgFilter，stdFilter）= ThresholdingAlgo （y：样本，滞后平均值：10，滞后标准差：1 00，阈值：2，influenceMean：0.5，influenceStd：0.1）可以提供更好的结果：

Would anyone have a good algorithm to measure peaks in growing time series data using Swift (v3)? So, detect peaks as the data is streaming in.

E.g. a Swift version of the smooth z-wave algorithm. That algorithm seems to be suitable.

I would need to detect the peaks as shown below. The data contains positive and negative numbers. Output should be a counter of the peaks, and/or true/false for that specific sample.

Sample dataset (summary of the last series):

let samples = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,
  -0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07, 
  0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18, 
  1.31, 0.66, 0.07, -1.62, -0.16, 0.67, 0.19, -0.42, 0.23, -0.05, -0.01,
  0.03, 0.06, 0.27, 0.15, -0.50, -1.18, 0.11, 1.30, 0.93, 0.16, -1.32, 
  -0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,
  -1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,
  0.12, 0.23, 0.29, -0.75, -0.95, 0.11, 1.51, 0.70, -0.30, -1.48, 0.13,
  0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,
  -0.01, 0.01, 0.02, 0.01]

Update: Thanks to Jean-Paul for the initial Swift port. But not sure the z-wave algo is the right one for this dataset. lag=10,threshold=3,influence=0.2 works fine for the last series of the dataset, but I have not been able to find a combination that comes close for the complete dataset.

The issues: with a big lag the first data samples are not included, I need one signal per peak and the algorithm would need further work to be made more efficient.

E.g. result for full dataset, using the Python code, and (e.g.) lag=5,threshold=2.5,influence=0.7 is missing peaks for series 1 and 2, and showing too many false positives in the quiet periods:

Full dataset (should result in 25 peaks):

let samples = [-1.38, -0.97, -1.20, -2.06, -2.26, -0.99, 0.11, -0.47, -0.95, -2.61, -0.88, -0.74, -1.12, -1.19, -1.12, -1.04, -0.72, -1.21, -2.61, -1.41, -0.23, -0.27, -0.43, -1.77, -2.75, -0.61, -0.73, -1.53, -1.02, -1.14, -1.12, -1.06, -0.78, -0.72, -2.41, -1.55, -0.01, -0.44, -0.47, -2.02, -1.66, -0.43, -0.93, -1.51, -0.86, -1.06, -1.10, -0.88, -0.84, -1.26, -2.59, -0.92, 0.29, -0.50, -1.31, -2.40, -0.88, -0.56, -1.09, -1.14, -1.09, -0.90, -0.99, -0.84, -0.75, -2.59, -1.34, -0.08, -0.36, -0.50, -1.89, -1.60, -0.55, -0.78, -1.46, -0.96, -0.97, -1.18, -0.98, -1.10, -1.07, -1.06, -1.79, -1.78, -1.54, -1.25, -1.00, -0.46, -0.27, -0.20, -0.15, -0.13, -0.11, -0.13, -0.09, -0.09, -0.05, 0.02, 0.20, -0.31, -1.35, -0.03, 1.34, 0.52, 0.80, -0.91, -1.26, -0.10, -0.10, 0.53, 0.93, 0.60, -0.83, -1.87, -0.21, 1.26, 0.44, 0.86, 0.73, -2.05, -1.66, 0.31, 1.04, 0.72, 0.63, -0.01, -2.14, -0.48, 0.77, 0.63, 0.58, 0.66, -1.01, -1.28, 0.18, 0.44, 0.09, -0.27, -0.06, 0.06, -0.18, -0.01, -0.08, -0.07, -0.06, -0.06, -0.07, -0.07, -0.06, -0.05, -0.04, -0.03, -0.02, -0.02, -0.03, -0.03, -0.01, 0.01, 0.00, 0.01, 0.05, 0.12, 0.16, 0.25, 0.29, -0.16, -0.69, -1.05, -0.84, -0.54, -0.07, 0.46, 1.12, 1.05, 0.77, 0.68, 0.63, 0.39, -0.96, -1.61, -0.68, -0.14, -0.03, 0.22, 0.31, 0.15, -0.02, 0.11, 0.14, 0.00, 0.04, 0.18, 0.27, 0.14, -0.05, -0.03, -0.08, -0.41, -0.94, -1.03, -0.50, 0.02, 0.52, 1.10, 1.03, 0.79, 0.69, 0.55, -0.34, -1.17, -0.89, -0.54, -0.22, 0.37, 0.47, 0.39, 0.23, 0.00, -0.02, 0.05, 0.10, 0.12, 0.09, 0.05, -0.12, -0.50, -0.89, -0.89, -0.48, 0.00, 0.43, 1.03, 0.95, 0.67, 0.64, 0.47, -0.07, -0.85, -1.02, -0.73, -0.08, 0.38, 0.46, 0.32, 0.15, 0.01, -0.01, 0.09, 0.20, 0.23, 0.19, 0.12, -0.50, -1.17, -0.97, -0.12, 0.15, 0.70, 1.31, 0.97, 0.45, 0.27, -0.73, -1.00, -0.52, -0.27, 0.10, 0.33, 0.34, 0.23, 0.07, -0.04, -0.27, -0.24, 0.10, 0.21, 0.05, -0.07, 0.04, 0.21, 0.29, 0.16, -0.45, -1.13, -0.93, -0.28, 0.04, 0.72, 1.35, 1.05, 0.56, 0.43, 0.17, -0.59, -1.38, -0.76, 0.10, 0.44, 0.46, 0.35, 0.12, -0.07, -0.05, -0.01, -0.07, -0.04, 0.01, 0.01, 0.06, 0.02, -0.03, -0.05, 0.00, 0.01, -0.02, -0.03, -0.02, -0.01, 0.00, -0.01, 0.00, -0.01, 0.00, -0.01, -0.01, 0.00, 0.01, -0.01, -0.01, 0.00, 0.00, 0.01, 0.01, 0.01, 0.04, 0.06, 0.05, 0.05, 0.04, 0.03, 0.00, -0.12, -0.16, -0.09, -0.01, 0.14, 0.07, 0.06, 0.00, -0.03, 0.00, 0.06, 0.06, -0.04, -0.11, -0.02, 0.13, 0.18, 0.21, 0.01, -0.31, -0.92, -1.35, -0.62, 0.03, 0.78, 1.36, 1.07, 0.59, 0.75, 0.42, -1.65, -3.16, -0.97, 0.24, 1.44, 1.50, 0.84, 0.47, 0.56, 0.40, -1.50, -2.71, -1.22, 0.01, 1.20, 1.55, 0.92, 0.44, 0.66, 0.73, -0.43, -2.34, -2.28, -0.72, 0.36, 1.41, 1.56, 0.89, 0.54, 0.67, 0.39, -1.78, -2.75, -1.07, -0.07, 1.16, 1.65, 0.80, 0.47, 0.73, 0.86, -0.24, -1.52, -1.68, -0.39, 0.02, 0.38, 0.60, 0.49, 0.02, -0.42, -0.31, -0.01, 0.08, 0.00, -0.07, -0.05, -0.01, -0.02, -0.04, -0.05, -0.02, -0.01, -0.02, -0.02, -0.03, -0.05, -0.04, -0.03, -0.01, -0.01, 0.00, -0.01, 0.00, 0.01, 0.00, 0.00, 0.00, 0.01, 0.01, -0.01, -0.03, -0.02, -0.01, 0.00, 0.00, 0.00, -0.01, 0.01, 0.00, -0.01, 0.02, 0.07, 0.15, 0.28, 0.31, 0.08, -0.26, -0.54, -0.96, -1.08, -0.27, 0.01, 0.45, 1.18, 1.07, 0.71, 0.65, 0.20, -0.80, -1.30, -0.74, -0.24, 0.29, 0.47, 0.34, 0.15, 0.02, 0.03, -0.02, -0.16, -0.13, 0.05, 0.09, -0.01, -0.08, -0.06, 0.03, 0.13, 0.19, 0.23, 0.18, 0.10, -0.07, -0.44, -0.91, -1.05, -0.64, -0.08, 0.50, 1.12, 1.35, 0.89, 0.58, 0.54, -0.58, -1.27, -1.20, -0.48, 0.19, 0.62, 0.62, 0.37, -0.01, -0.35, -0.33, 0.07, 0.29, 0.10, -0.14, -0.10, 0.07, 0.07, 0.01, 0.03, 0.09, 0.20, 0.32, 0.26, -0.02, -0.32, -0.78, -1.25, -0.93, -0.16, 0.30, 0.88, 1.40, 1.14, 0.72, 0.48, -0.54, -1.21, -1.13, -0.41, 0.18, 0.51, 0.53, 0.36, 0.11, -0.03, -0.09, -0.28, -0.11, 0.11, 0.15, 0.04, -0.08, -0.04, 0.04, 0.09, 0.16, 0.26, 0.43, 0.09, -0.88, -1.46, -0.64, -0.16, 0.43, 1.37, 1.34, 0.84, 0.52, -0.17, -0.87, -1.22, -0.76, 0.03, 0.47, 0.60, 0.36, 0.04, -0.09, -0.03, 0.02, -0.04, 0.04, 0.12, 0.13, 0.19, 0.27, 0.31, 0.18, -0.42, -0.99, -1.13, -0.75, -0.22, 0.50, 1.42, 1.41, 0.98, 0.51, 0.29, -0.69, -1.59, -0.88, -0.13, 0.31, 0.49, 0.46, 0.30, 0.05, -0.08, -0.03, 0.01, -0.04, -0.06, 0.02, 0.03, 0.01, -0.02, 0.01, 0.04, 0.06, 0.04, 0.03, 0.02, 0.03, 0.03, 0.01, -0.01, 0.00, 0.02, 0.00, 0.02, 0.02, 0.02, -0.02, -0.01, 0.02, 0.02, 0.01, 0.02, 0.02, 0.02, 0.02, 0.04, 0.03, 0.01, 0.01, 0.02, 0.01, 0.01, 0.01, 0.02, 0.01, 0.00, 0.01, 0.01, 0.00, 0.00, 0.01, 0.00, 0.00, 0.01, 0.00, 0.02, 0.00, 0.00, 0.01, 0.01, 0.00, 0.00, 0.01, 0.01, 0.00, 0.00, 0.00, 0.01, 0.01, 0.00, 0.01, 0.00, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.01, 0.01, 0.01, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00]

I am therefore not sure the z-wave algorithm is the right approach for this kind of dataset.

解决方案

Translation of smooth z-score algo into Swift

Well, to quickly help you out: here is a translation of the algo into Swift: Demo in Swift Sandbox

Warning: I am by no means a swift programmer, so there could be mistakes in there!

Also note that I have turned off negative signals, as for OP's purpose we only want positive signals.

Swift code:

import Glibc // or Darwin/ Foundation/ Cocoa/ UIKit (depending on OS)

// Function to calculate the arithmetic mean
func arithmeticMean(array: [Double]) -> Double {
    var total: Double = 0
    for number in array {
        total += number
    }
    return total / Double(array.count)
}

// Function to calculate the standard deviation
func standardDeviation(array: [Double]) -> Double
{
    let length = Double(array.count)
    let avg = array.reduce(0, {$0 + $1}) / length
    let sumOfSquaredAvgDiff = array.map { pow($0 - avg, 2.0)}.reduce(0, {$0 + $1})
    return sqrt(sumOfSquaredAvgDiff / length)
}

// Function to extract some range from an array
func subArray<T>(array: [T], s: Int, e: Int) -> [T] {
    if e > array.count {
        return []
    }
    return Array(array[s..<min(e, array.count)])
}

// Smooth z-score thresholding filter
func ThresholdingAlgo(y: [Double],lag: Int,threshold: Double,influence: Double) -> ([Int],[Double],[Double]) {

    // Create arrays
    var signals   = Array(repeating: 0, count: y.count)
    var filteredY = Array(repeating: 0.0, count: y.count)
    var avgFilter = Array(repeating: 0.0, count: y.count)
    var stdFilter = Array(repeating: 0.0, count: y.count)

    // Initialise variables
    for i in 0...lag-1 {
        signals[i] = 0
        filteredY[i] = y[i]
    }

    // Start filter
    avgFilter[lag-1] = arithmeticMean(array: subArray(array: y, s: 0, e: lag-1))
    stdFilter[lag-1] = standardDeviation(array: subArray(array: y, s: 0, e: lag-1))

    for i in lag...y.count-1 {
        if abs(y[i] - avgFilter[i-1]) > threshold*stdFilter[i-1] {
            if y[i] > avgFilter[i-1] {
                signals[i] = 1      // Positive signal
            } else {
                // Negative signals are turned off for this application
                //signals[i] = -1       // Negative signal
            }
            filteredY[i] = influence*y[i] + (1-influence)*filteredY[i-1]
        } else {
            signals[i] = 0          // No signal
            filteredY[i] = y[i]
        }
        // Adjust the filters
        avgFilter[i] = arithmeticMean(array: subArray(array: filteredY, s: i-lag, e: i))
        stdFilter[i] = standardDeviation(array: subArray(array: filteredY, s: i-lag, e: i))
    }

    return (signals,avgFilter,stdFilter)
}

// Demo
let samples = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,
  -0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07, 
  0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18, 
  1.31, 0.66, 0.07, -1.62, -0.16, 0.67, 0.19, -0.42, 0.23, -0.05, -0.01,
  0.03, 0.06, 0.27, 0.15, -0.50, -1.18, 0.11, 1.30, 0.93, 0.16, -1.32, 
  -0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,
  -1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,
  0.12, 0.23, 0.29, -0.75, -0.95, 0.11, 1.51, 0.70, -0.30, -1.48, 0.13,
  0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,
  -0.01, 0.01, 0.02, 0.01]

// Run filter
let (signals,avgFilter,stdFilter) = ThresholdingAlgo(y: samples, lag: 10, threshold: 3, influence: 0.2)
// Print output to console
print("\nOutput: \n ")
for i in 0...signals.count - 1 {
    print("Data point \(i)\t\t sample: \(samples[i]) \t signal: \(signals[i])\n")
}

// Raw data for creating a plot in Excel
print("\n \n Raw data for creating a plot in Excel: \n ")
for i in 0...signals.count - 1 {
    print("\(i+1)\t\(samples[i])\t\(signals[i])\t\(avgFilter[i])\t\(stdFilter[i])\n")
}

With the result for the sample data (for lag = 10, threshold = 3, influence = 0.2):

Update

You can improve the performance of the algorithm by using different values for the lag of the mean and the standard deviation. E.g.:

// Smooth z-score thresholding filter
func ThresholdingAlgo(y: [Double], lagMean: Int, lagStd: Int, threshold: Double, influenceMean: Double, influenceStd: Double) -> ([Int],[Double],[Double]) {

    // Create arrays
    var signals   = Array(repeating: 0, count: y.count)
    var filteredYmean = Array(repeating: 0.0, count: y.count)
    var filteredYstd = Array(repeating: 0.0, count: y.count)
    var avgFilter = Array(repeating: 0.0, count: y.count)
    var stdFilter = Array(repeating: 0.0, count: y.count)

    // Initialise variables
    for i in 0...lagMean-1 {
        signals[i] = 0
        filteredYmean[i] = y[i]
        filteredYstd[i] = y[i]
    }

    // Start filter
    avgFilter[lagMean-1] = arithmeticMean(array: subArray(array: y, s: 0, e: lagMean-1))
    stdFilter[lagStd-1] = standardDeviation(array: subArray(array: y, s: 0, e: lagStd-1))

    for i in max(lagMean,lagStd)...y.count-1 {
        if abs(y[i] - avgFilter[i-1]) > threshold*stdFilter[i-1] {
            if y[i] > avgFilter[i-1] {
                signals[i] = 1      // Positive signal
            } else {
                signals[i] = -1       // Negative signal
            }
            filteredYmean[i] = influenceMean*y[i] + (1-influenceMean)*filteredYmean[i-1]
            filteredYstd[i] = influenceStd*y[i] + (1-influenceStd)*filteredYstd[i-1]
        } else {
            signals[i] = 0          // No signal
            filteredYmean[i] = y[i]
            filteredYstd[i] = y[i]
        }
        // Adjust the filters
        avgFilter[i] = arithmeticMean(array: subArray(array: filteredYmean, s: i-lagMean, e: i))
        stdFilter[i] = standardDeviation(array: subArray(array: filteredYstd, s: i-lagStd, e: i))
    }

    return (signals,avgFilter,stdFilter)
}

Then using for example let (signals,avgFilter,stdFilter) = ThresholdingAlgo(y: samples, lagMean: 10, lagStd: 100, threshold: 2, influenceMean: 0.5, influenceStd: 0.1) can give a lot better results:

DEMO

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