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 69.46% per annum.
- AMZN price at the close of April 22, 2024 was $177.23 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 102.81% per annum.
- AMZN price at the close of April 22, 2024 was lower than the bottom border of the secondary price channel by $1.87 (1.05%). This indicates a possible reversal in the secondary trend direction.
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 18, 2022
End date: April 22, 2024
a = 2.5743
b = 0.0014
s = 0.0547
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 69.46%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0547) – 1
= 24.45%
November 18, 2022 calculations
Top border of price channel:
Exp(Y903)
= Exp(a + b × X903 + 2 × s)
= Exp(a + b × 1,305 + 2 × s)
= Exp(2.5743 + 0.0014 × 1,305 + 2 × 0.0547)
= Exp(4.5695)
= $96.49
Bottom border of price channel:
Exp(Y903)
= Exp(a + b × X903 – 2 × s)
= Exp(a + b × 1,305 – 2 × s)
= Exp(2.5743 + 0.0014 × 1,305 – 2 × 0.0547)
= Exp(4.3507)
= $77.54
April 22, 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(2.5743 + 0.0014 × 1,826 + 2 × 0.0547)
= Exp(5.3223)
= $204.86
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.5743 + 0.0014 × 1,826 – 2 × 0.0547)
= Exp(5.1036)
= $164.61
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 69.46% per annum.
- AMZN price at the close of April 22, 2024 was $177.23 and was inside the primary price channel.
Secondary Trend
Start date: September 26, 2023
End date: April 22, 2024
a = 1.7084
b = 0.0019
s = 0.0289
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0019) – 1
= 102.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0289) – 1
= 12.27%
September 26, 2023 calculations
Top border of price channel:
Exp(Y1,115)
= Exp(a + b × X1,115 + 2 × s)
= Exp(a + b × 1,617 + 2 × s)
= Exp(1.7084 + 0.0019 × 1,617 + 2 × 0.0289)
= Exp(4.8988)
= $134.13
Bottom border of price channel:
Exp(Y1,115)
= Exp(a + b × X1,115 – 2 × s)
= Exp(a + b × 1,617 – 2 × s)
= Exp(1.7084 + 0.0019 × 1,617 – 2 × 0.0289)
= Exp(4.7831)
= $119.47
April 22, 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(1.7084 + 0.0019 × 1,826 + 2 × 0.0289)
= Exp(5.3037)
= $201.08
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.7084 + 0.0019 × 1,826 – 2 × 0.0289)
= Exp(5.1880)
= $179.10
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 102.81% per annum.
- AMZN price at the close of April 22, 2024 was lower than the bottom border of the secondary price channel by $1.87 (1.05%). This indicates a possible reversal in the secondary trend direction.
- 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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