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 52.75% per annum.
- BKNG price at the close of May 20, 2024 was $3,768.62 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.40% per annum.
- BKNG 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 BKNG 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: June 16, 2022
End date: May 20, 2024
a = 6.1604
b = 0.0012
s = 0.0674
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 52.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0674) – 1
= 30.93%
June 16, 2022 calculations
Top border of price channel:
Exp(Y775)
= Exp(a + b × X775 + 2 × s)
= Exp(a + b × 1,122 + 2 × s)
= Exp(6.1604 + 0.0012 × 1,122 + 2 × 0.0674)
= Exp(7.5975)
= $1,993.16
Bottom border of price channel:
Exp(Y775)
= Exp(a + b × X775 – 2 × s)
= Exp(a + b × 1,122 – 2 × s)
= Exp(6.1604 + 0.0012 × 1,122 – 2 × 0.0674)
= Exp(7.3280)
= $1,522.28
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(6.1604 + 0.0012 × 1,826 + 2 × 0.0674)
= Exp(8.4146)
= $4,512.48
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.1604 + 0.0012 × 1,826 – 2 × 0.0674)
= Exp(8.1451)
= $3,446.42
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 52.75% per annum.
- BKNG price at the close of May 20, 2024 was $3,768.62 and was inside the primary price channel.
Secondary Trend
Start date: December 12, 2023
End date: May 20, 2024
a = 7.8358
b = 0.0002
s = 0.0300
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0300) – 1
= 12.75%
December 12, 2023 calculations
Top border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 + 2 × s)
= Exp(a + b × 1,666 + 2 × s)
= Exp(7.8358 + 0.0002 × 1,666 + 2 × 0.0300)
= Exp(8.2218)
= $3,721.23
Bottom border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 – 2 × s)
= Exp(a + b × 1,666 – 2 × s)
= Exp(7.8358 + 0.0002 × 1,666 – 2 × 0.0300)
= Exp(8.1018)
= $3,300.40
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(7.8358 + 0.0002 × 1,826 + 2 × 0.0300)
= Exp(8.2531)
= $3,839.58
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.8358 + 0.0002 × 1,826 – 2 × 0.0300)
= Exp(8.1331)
= $3,405.36
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.40% per annum.
- BKNG 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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