时序数据异常检测相关的问题记录

量化曲线的波动情况，即如何判断曲线是否平滑？

# 求导，统计数据波动的次数，跟阈值作比较
def is_fluctuating(series):
    ets = series[-1][0]
    raw = [item[1] for item in series if item[0] >= (ets - 86400)]
    fluctuation = np.diff(raw) > 0
    count = 0
    for idx in range(0, len(fluctuation)-1):
        if fluctuation[idx] != fluctuation[idx+1]:
            count = count + 1
    return count/len(raw) > 0.5

# 指数加权移动平均
def ewma(series):
    s = pd.Series([ ii[1] for ii in series ])
    ewma = pd.Series.ewm(s, ignore_na=False, min_periods=0, adjust=True, com=2).mean()
    nums = [round(num, 2) for num in ewma.to_list()]
    ewma_series = []
    for idx in range(0, len(series)):
        ewma_series.append([series[idx][0], nums[idx]])
    return ewma_series

如何判断两条曲线是否"胶着"在一起？

# 取指定周期的数据做差分
def check_intersect(timeseries):
    period = 3600
    # Step01 计算之前需要处理数据缺失的问题，避免出现ValueError: operands could not be broadcast together with shapes
    ets = timeseries[-1][0]
    raw_today = [ii[1] for ii in timeseries if ets - period < ii[0] <= ets]
    raw_yesterday = [ii[1] for ii in timeseries if ets - 86400 - period < ii[0] <= ets - 86400]
    raw_week = [ii[1] for ii in timeseries if ets - 86400 * 7 - period < ii[0] <= ets - 86400 * 7]
    if len(raw_today) < 2 or len(raw_yesterday) < 2 or len(raw_week) < 2:
        return False
    granularity = 60 if len(timeseries) > 2305 else 300  # 粒度是1分钟还是5分钟
    count = period / granularity
    while len(raw_today) < count:
        raw_today.append(np.mean(raw_today))
    while len(raw_yesterday) < count:
        raw_yesterday.append(np.mean(raw_yesterday))
    while len(raw_week) < count:
        raw_week.append(np.mean(raw_week))
    # Step02 计算当前数据和历史数据的偏离程度
    arr_today = np.array(raw_today)
    arr_yesterday = np.array(raw_yesterday)
    arr_week = np.array(raw_week)
    t2y = arr_today - arr_yesterday
    t2w = arr_today - arr_week
    percent2y = t2y / arr_today
    percent2w = t2w / arr_today
    threshold = 0.1
    if np.mean(np.abs(percent2y)) < threshold or np.mean(np.abs(percent2w)) < threshold:
        return True
    return False

判断曲线是否是周期性曲线，并计算出其周期。

# 傅里叶变换，时域转换为频域。