Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 2.77% per annum.
- LOW price at the close of May 20, 2024 was $229.17 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.99% per annum.
- LOW price at the close of May 20, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of LOW price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: March 25, 2021
End date: February 22, 2024
a = 5.2117
b = 0.0001
s = 0.0824
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0824) – 1
= 39.02%
March 25, 2021 calculations
Top border of price channel:
Exp(Y465)
= Exp(a + b × X465 + 2 × s)
= Exp(a + b × 674 + 2 × s)
= Exp(5.2117 + 0.0001 × 674 + 2 × 0.0824)
= Exp(5.4270)
= $227.46
Bottom border of price channel:
Exp(Y465)
= Exp(a + b × X465 – 2 × s)
= Exp(a + b × 674 – 2 × s)
= Exp(5.2117 + 0.0001 × 674 – 2 × 0.0824)
= Exp(5.0976)
= $163.62
February 22, 2024 calculations
Top border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 + 2 × s)
= Exp(a + b × 1,738 + 2 × s)
= Exp(5.2117 + 0.0001 × 1,738 + 2 × 0.0824)
= Exp(5.5068)
= $246.36
Bottom border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 – 2 × s)
= Exp(a + b × 1,738 – 2 × s)
= Exp(5.2117 + 0.0001 × 1,738 – 2 × 0.0824)
= Exp(5.1773)
= $177.21
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 2.77% per annum.
- LOW price at the close of May 20, 2024 was $229.17 and was inside the primary price channel.
Secondary Trend
Start date: May 5, 2022
End date: May 20, 2024
a = 4.8311
b = 0.0003
s = 0.0556
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0556) – 1
= 24.90%
May 5, 2022 calculations
Top border of price channel:
Exp(Y746)
= Exp(a + b × X746 + 2 × s)
= Exp(a + b × 1,080 + 2 × s)
= Exp(4.8311 + 0.0003 × 1,080 + 2 × 0.0556)
= Exp(5.3035)
= $201.05
Bottom border of price channel:
Exp(Y746)
= Exp(a + b × X746 – 2 × s)
= Exp(a + b × 1,080 – 2 × s)
= Exp(4.8311 + 0.0003 × 1,080 – 2 × 0.0556)
= Exp(5.0812)
= $160.97
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.8311 + 0.0003 × 1,826 + 2 × 0.0556)
= Exp(5.5531)
= $258.04
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.8311 + 0.0003 × 1,826 – 2 × 0.0556)
= Exp(5.3308)
= $206.60
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.99% per annum.
- LOW price at the close of May 20, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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