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# System prepended metadata

title: part2 week1

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# part2 week1
## Sequences, Time Series and Prediction week1
### Ｗhat exactly is a time series?
> It's typically defined as an ordered sequence of values that are usually equally spaced over time.
> 隨著時間有固定間隔、順序的序列值

### Univariate v.s. Multivariate Time Series
> 單變量可觀察趨勢、多變量則可能存在相關性、取得更多資訊
![](https://i.imgur.com/ncXfByv.png)

### 時間序列的分析
* 預測未來值
* 插補過去缺失值(imputation)
* 異常檢測(Anomaly detection)
* 聲紋辨識(STT)

### common patterns in time series
* 趨勢(trend)
* 季節性(seasonality)
![](https://i.imgur.com/b7s1Vq7.png)
* 白噪音(white noise)
* 自相關(autocorrelation)
![](https://i.imgur.com/JvHQiLB.png)
  > Often a time series like this is described as having memory as steps are dependent on previous ones.
  > The spikes which are unpredictable are often called Innovations.

### stationary time series
機器學習是在發現行為模式(patterns)，但要是這些行為模式在未來同樣會出現才有用，這也反應抓取的資料區間不是越長越好，而是固定的行為模式在過去、未來存在關聯。
![](https://i.imgur.com/B2fr7JV.jpg)

> If this were stock, price then maybe it was a big financial crisis or a big scandal or perhaps a disruptive technological breakthrough causing a massive change. After that the time series started to trend downward without any clear seasonality. We'll typically call this a non-stationary time series.
### Train, validation and test sets
* 需要確認Train,validation and test sets都有涵蓋相同的趨勢變化(trend, seasonality,...)
* roll-forward partitioning vs. fixed partition
 fixed partition: 固定時間窗格(後續主要以此方法做介紹)
 ![](https://i.imgur.com/6ku4HgV.jpg)
 roll-forward partitioning: 動態調整時間窗格
 ![](https://i.imgur.com/dFv7bUP.png)
### Metrics for evaluating performance
* 衡量模型成效的各種指標(errors, mse, rmse, mae, mape)
* MAPE: 平均絕對百分比誤差(P是百分比的意思)
註:資料集當中有0的資料會導致無法算出結果

![](https://i.imgur.com/m19PD1d.png)

### Moving average and differencing
* 比較Naive, MA, differencing各方法的成效(mae)
naive:5.9
![](https://i.imgur.com/ld50DbF.jpg)
MA(30): 7.14
![](https://i.imgur.com/3oEojFV.jpg)
differencing: 5.8
![](https://i.imgur.com/6tlDbeQ.jpg)
MA(30)+differencing: 4.5
![](https://i.imgur.com/PMb1iN7.jpg)
* 進入deep learning之前記得先試試這些統計方法

### Trailing versus centered window
* centered window: 過去+未來預測現在(此方法無法預測未來的值)
* Trailing window: 純粹用過去資料來預測現在
