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 46.81% per annum.
- GOOG price at the close of April 23, 2024 was $159.92 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 27.36% per annum.
- GOOG price at the close of April 23, 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 GOOG 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: October 26, 2022
End date: April 23, 2024
a = 3.1559
b = 0.0011
s = 0.0581
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 46.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0581) – 1
= 26.15%
October 26, 2022 calculations
Top border of price channel:
Exp(Y885)
= Exp(a + b × X885 + 2 × s)
= Exp(a + b × 1,281 + 2 × s)
= Exp(3.1559 + 0.0011 × 1,281 + 2 × 0.0581)
= Exp(4.6195)
= $101.44
Bottom border of price channel:
Exp(Y885)
= Exp(a + b × X885 – 2 × s)
= Exp(a + b × 1,281 – 2 × s)
= Exp(3.1559 + 0.0011 × 1,281 – 2 × 0.0581)
= Exp(4.3872)
= $80.41
April 23, 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(3.1559 + 0.0011 × 1,826 + 2 × 0.0581)
= Exp(5.1927)
= $179.96
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.1559 + 0.0011 × 1,826 – 2 × 0.0581)
= Exp(4.9604)
= $142.66
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 46.81% per annum.
- GOOG price at the close of April 23, 2024 was $159.92 and was inside the primary price channel.
Secondary Trend
Start date: May 11, 2023
End date: April 23, 2024
a = 3.8154
b = 0.0007
s = 0.0363
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 27.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0363) – 1
= 15.61%
May 11, 2023 calculations
Top border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 + 2 × s)
= Exp(a + b × 1,478 + 2 × s)
= Exp(3.8154 + 0.0007 × 1,478 + 2 × 0.0363)
= Exp(4.8671)
= $129.95
Bottom border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 – 2 × s)
= Exp(a + b × 1,478 – 2 × s)
= Exp(3.8154 + 0.0007 × 1,478 – 2 × 0.0363)
= Exp(4.7221)
= $112.41
April 23, 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(3.8154 + 0.0007 × 1,826 + 2 × 0.0363)
= Exp(5.0977)
= $163.64
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.8154 + 0.0007 × 1,826 – 2 × 0.0363)
= Exp(4.9527)
= $141.55
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 27.36% per annum.
- GOOG price at the close of April 23, 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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