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 55.01% per annum.
- BKNG price at the close of April 24, 2024 was $3,517.52 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.93% per annum.
- BKNG price at the close of April 24, 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: April 12, 2024
a = 6.0749
b = 0.0012
s = 0.0660
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 55.01%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0660) – 1
= 30.22%
June 16, 2022 calculations
Top border of price channel:
Exp(Y793)
= Exp(a + b × X793 + 2 × s)
= Exp(a + b × 1,148 + 2 × s)
= Exp(6.0749 + 0.0012 × 1,148 + 2 × 0.0660)
= Exp(7.5856)
= $1,969.62
Bottom border of price channel:
Exp(Y793)
= Exp(a + b × X793 – 2 × s)
= Exp(a + b × 1,148 – 2 × s)
= Exp(6.0749 + 0.0012 × 1,148 – 2 × 0.0660)
= Exp(7.3216)
= $1,512.56
April 12, 2024 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,814 + 2 × s)
= Exp(6.0749 + 0.0012 × 1,814 + 2 × 0.0660)
= Exp(8.3854)
= $4,382.60
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,814 – 2 × s)
= Exp(6.0749 + 0.0012 × 1,814 – 2 × 0.0660)
= Exp(8.1214)
= $3,365.60
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 55.01% per annum.
- BKNG price at the close of April 24, 2024 was $3,517.52 and was inside the primary price channel.
Secondary Trend
Start date: December 13, 2023
End date: April 24, 2024
a = 8.0346
b = 0.0001
s = 0.0285
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0285) – 1
= 12.07%
December 13, 2023 calculations
Top border of price channel:
Exp(Y1,168)
= Exp(a + b × X1,168 + 2 × s)
= Exp(a + b × 1,693 + 2 × s)
= Exp(8.0346 + 0.0001 × 1,693 + 2 × 0.0285)
= Exp(8.2258)
= $3,736.01
Bottom border of price channel:
Exp(Y1,168)
= Exp(a + b × X1,168 – 2 × s)
= Exp(a + b × 1,693 – 2 × s)
= Exp(8.0346 + 0.0001 × 1,693 – 2 × 0.0285)
= Exp(8.1118)
= $3,333.56
April 24, 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(8.0346 + 0.0001 × 1,826 + 2 × 0.0285)
= Exp(8.2363)
= $3,775.60
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(8.0346 + 0.0001 × 1,826 – 2 × 0.0285)
= Exp(8.1223)
= $3,368.88
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.93% per annum.
- BKNG price at the close of April 24, 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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