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 64.66% per annum.
- AMZN price at the close of July 26, 2024 was $182.50 and was lower than the bottom border of the primary price channel by $0.99 (0.54%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 26.20% per annum.
- AMZN price at the close of July 26, 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 AMZN 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: November 2, 2022
End date: July 17, 2024
a = 2.8291
b = 0.0014
s = 0.0545
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 64.66%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0545) – 1
= 24.37%
November 2, 2022 calculations
Top border of price channel:
Exp(Y824)
= Exp(a + b × X824 + 2 × s)
= Exp(a + b × 1,192 + 2 × s)
= Exp(2.8291 + 0.0014 × 1,192 + 2 × 0.0545)
= Exp(4.5667)
= $96.23
Bottom border of price channel:
Exp(Y824)
= Exp(a + b × X824 – 2 × s)
= Exp(a + b × 1,192 – 2 × s)
= Exp(2.8291 + 0.0014 × 1,192 – 2 × 0.0545)
= Exp(4.3487)
= $77.37
July 17, 2024 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,815 + 2 × s)
= Exp(2.8291 + 0.0014 × 1,815 + 2 × 0.0545)
= Exp(5.4179)
= $225.41
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,815 – 2 × s)
= Exp(2.8291 + 0.0014 × 1,815 – 2 × 0.0545)
= Exp(5.1999)
= $181.25
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 64.66% per annum.
- AMZN price at the close of July 26, 2024 was $182.50 and was lower than the bottom border of the primary price channel by $0.99 (0.54%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 2, 2024
End date: July 26, 2024
a = 4.0949
b = 0.0006
s = 0.0259
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 26.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0259) – 1
= 10.92%
February 2, 2024 calculations
Top border of price channel:
Exp(Y1,137)
= Exp(a + b × X1,137 + 2 × s)
= Exp(a + b × 1,649 + 2 × s)
= Exp(4.0949 + 0.0006 × 1,649 + 2 × 0.0259)
= Exp(5.1981)
= $180.94
Bottom border of price channel:
Exp(Y1,137)
= Exp(a + b × X1,137 – 2 × s)
= Exp(a + b × 1,649 – 2 × s)
= Exp(4.0949 + 0.0006 × 1,649 – 2 × 0.0259)
= Exp(5.0945)
= $163.12
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.0949 + 0.0006 × 1,824 + 2 × 0.0259)
= Exp(5.3097)
= $202.29
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.0949 + 0.0006 × 1,824 – 2 × 0.0259)
= Exp(5.2061)
= $182.38
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 26.20% per annum.
- AMZN price at the close of July 26, 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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